Test: Savings And Interest- 2 - GMAT MCQ

Given:

Fund A - 2012

• P = 100,000
• R = -20%
• T = 1 year
• Fund B – 2013 - 14
  • 2013
  • Principal, B = Amount in Fund A at the end of 2012
  • R = 20%
  • T = 1 year
• 2014
  • Principal, B = Amount in Fund B at the end of 2013
  • R = 10%
  • T = 1 year

To Find: % Money growth from 2012 to 2014

Approach:

% Money Growth =
We know the Invested Principal in 2012
So, to answer the question, we need to find the Amount in 2014
1.
2. To find ‘Amount in 2014’, we need to know B
To know B , we need to know B . So, we’ll start working towards the
answer by calculating B .

Working out:

Looking at the answer choices, we see that the correct answer is Option C

Step 1 & 2: Understand Question and Draw Inference

Step 3 : Analyze Statement 1 independent

Statement 1 says that ‘The value of p was between 25 and 30, inclusive’

• So, the answer to the question ‘Is p > 43?’ is NO

Since Statement 1 leads to a unique answer to the question, it is sufficient

Step 4 : Analyze Statement 2 independent

Statement 2 says that ‘The total interest earned by the two accounts during 2015 was $66’

• (Interest earned by Account X) + (Interest earned by Account Y) = 66
• 
• This is a linear equation with only 1 unknown, p. So, by solving this equation, we will be able to find the value of p
• Once we know the value of p, we can answer the question ‘Is p > 43?’
• So, Statement 2 also is sufficient to answer the question

Step 5: Analyze Both Statements Together (if needed)

Since we’ve already arrived at a unique answer in Steps 3 and 4, this step is not required
Answer: Option D

Given:

• Principal = $200,000
• Rate of return = r% per annum, compounded semi-annually
• Time = 1 year

= 2 half- years (that is, 2 periods of compounding)

• Amount = $220,500

To Find: r = ?

Approach:

1. Since r is the annual rate of return but compounding happens every 6-months, the rate of return for 6 months = r/2 %
2. We are given the amount that the principal grows into in 2 periods of compounding. Using this information, we can find the rate of return for 6 months​

Working out:

• Upon taking square roots on both sides of this equation, 2 cases arise:

• The negative value of r indicates degrowth in the principal (that is, instead of increasing, the invested principal decreased and the amount was less than the invested principal). However, this contradicts the given information (Amount is given to be $220,500, which is greater than the invested principal).
• Therefore, this case is rejected
• Hence, we get a unique value of r = 10%
  Looking at the answer choices, we see that the correct answer is Option C

Given:

• Principal = $62,500
• Rate of interest = 16% per annum, compounded quarterly
  • So, rate of interest per quarter =
• Let the time period of investment be t quarters
• Interest earned in t quarters = $5,100
  • So, Amount = $62,500 + $5,100 = $67,600

To Find: Time Period of Investment in Months

• = 3t months (since each quarter has 3 months)

Approach:

1. To find the value of 3t, we need to know the value of t, that is the number of quarters in which the investment earns the given interest
2. We are given the principal, and we have deduced the final amount and the quarterly rate of interest. We will use this information to find the value of

Working out:

• Since both sides of the above equation have the same base, the powers of the base on both sides of the equation will be equal as well.
• So, t = 2
• Remember that t denotes the number of quarters and the answer requires the number of months.
• The number of months in which the investment earns the given interest = 3t = 3*2 = 6 months
  Looking at the answer choices, we see that the correct answer is Option D

Given:

• Principal = $200,000
• Rate of interest = r% per annum, compounded quarterly
• Time Period = 6 months
  • = 2 quarters (that is, 2 periods of compounding)
• Growth in Principal = $88,000
  • So, Amount = $200,000 + $88,000 = $288,000

To Find: r = ?

Approach:

1. Since r is the annual rate of return but compounding happens every quarter, the rate of return per quarter  = r/4 %
2. We are given the amount that the principal grows into in 2 periods of compounding. Using this information, we can find the rate of return per quarter

Working out:

• The negative value of r indicates degrowth in the principal (that is, instead of increasing, the invested principal decreased and the amount was less than the invested principal). However, this contradicts the given information (we’re given that the invested principal grew by $88,000).
• Therefore, this case is rejected

So, r = 80%

Looking at the answer choices, we see that the correct answer is Option E

Given:

• Money borrowed by Dan (P) = $10,000
• Rate of compound interest charged by Lucy (R) = 10% p.a., compounded annually
• Total amount paid back by Dan (A) = $13,310

To Find:

Number of years Dan takes to pay his entire debt to Lucy.
Let the number of years be n.
Now we know that the formula for paying the total debt (which is paid at
a compounded interest) is given by  where  R=10%p.a.; P=$10,000 & A=$13,310
So we know all the values to be used in the above formula except n → no. of years, which is to be calculated as desired in the question.

Approach:

• We know the values of A, R & P and also the total debt paid as given by the formula 
• Putting the values of knowns in the above formula, we will be able to calculate the value of n from the above formula.

Working out:

Comparing both sides of the equation (as both are raised to sake base  

 we get
n=3 years.

Answer

• Hence number of years Dan takes to pay his entire debt is 3 years
• Hence answer option E is correct

Given:

• Let the money saved by Jane in year 2014 be SJ₂₀₁₄ . Given SJ₂₀₁₄ = $2000
• Let the money saved by Nancy in year 2014 be SN₂₀₁₄ . Given SN₂₀₁₄ = $2000
• Percentage more money saved by Jane in year 2015 than the money saved by Jane in year 2014 is 10%. Let this percentage be x. So we have → x = 10%
• Percentage less money saved by Nancy in year 2015 than the money saved by Jane in year 2015 is 15%. Let this percentage by y. So we have → y = 15%
• Let the money saved by Jane in year 2015 be SJ₂₀₁₅
• Let the money saved by Nancy in year 2015 be SN₂₀₁₅

_​To Find:

• We have to calculate how much less money does Nancy save in year 2015 than in year 2014.
• In other words, we have to calculate → SN₂₀₁₄ - SN₂₀₁₅
• Thus we somehow need to find the value of SN₂₀₁₅ to be able to calculate the difference in the savings of Nancy in the two years, as asked in the question. (We already are given the value of SN₂₀₁₄ = $2000 )

Approach:

• In order to find → SN₂₀₁₅ , we will first work out on the savings made by Jane (SJ₂₀₁₅ ) in year 2015.
• To find the values of savings made by Jane in year 2015 (SJ₂₀₁₅ ), we will make use of the savings made by Jane in year 2014 and the percentage increase in savings (x) from year 2014 to year 2015, and use the relation ⇒ SJ₂₀₁₅ = SJ₂₀₁₄ + x*SJ₂₀₁₄
• After calculating the value of SJ₂₀₁₅ and from the percentage of less money (y) saved by Nancy in year 2015 from the money saved by Jane in year 2015, we will be able to calculate the savings of Nancy in year 2015 → SN₂₀₁₅ , by using the relation ⇒ SN₂₀₁₅ = SJ₂₀₁₅ - y*SJ₂₀₁₅
• Once we know the savings of Nancy in year 2015 → SN₂₀₁₅ , we can finally calculate the value of SN₂₀₁₅ - SN₂₀₁₄ , as desired in the question

Working out:

Answer :

• Hence the money saved by Nancy in year 2015 is $130 less than the money saved by her in year 2014.
• Hence answer option D is correct.

Step 1 & 2: Understand Question and Draw Inference

Given:

• Total investment = $1000
  • Let investment in A = a dollars
  • So, investment in B = 1000 – a dollars
• Total interest earned = 10% per annum
  • = 10% of 1000 = $100 per annum

To find :a = ?

• Let Investment A give a return of x percent and Investment B give a return of y percent.
• Since Total interest earned = $100, we can write:
  • Interest earned from Investment A + Interest earned from Investment B = 100

• Thus, in order to know the value of a, we need to know the value of x and y.

Step 3 : Analyze Statement 1 independent

(1) Had he increased the share of mutual fund A in his total investment by 50 percent, he would have received a combined yearly return of 11 percent

• Note that the amount of total investment still remains $1000 only. Only the allocation of this amount between investments A and B has changed
  • So, new investment in A = 1.5a
  • New investment in B = 1000 – 1.5a
  • Given: Combined yearly return = 11% of $1000 = $110
    • (Return from Investment A) + (Return from Investment B) = 110

​

• This equation has 3 unknowns. Therefore, it is not sufficient to determine a unique value of a

Step 4 : Analyze Statement 2 independent

2) He received a return of 8 percent from mutual fund B

This equation has 2 unknowns. Not sufficient to find a unique value of x.

Step 5: Analyze Both Statements Together (if needed)

• Substituting y = 8 in (III) we get:
  • ax - 8a = 2000
• This is the same as Equation (IV)

So, even after both statements together, we cannot find a unique value of a.

Answer: Option E

Given:

• Let the combined earnings of the couple in the 1 year be t.
• So, the given information can be tabulated as follows :

​

To Find: Approximate percentage by which the 2^nd year interest is greater than the 1^st year interest

Approach:

1. 
   • So, to answer the question, we need to find the (combined) 1 year interest and the (combined) 2^nd year interest
2. For the 1^st year, we know the savings principal, interest rate and time for both the wife’s investment and the husband’s investment. Therefore, we can easily find the interest earned by wife and by the husband. And, by adding these 2 interests, we’ll get the combined 1^st year interest. The same process can be followed for the 2^nd year as well. We have all the required information points.

Working out:

• Calculating Year 2 Combined Interest

• The actual value will be slightly less than 64% since the denominator 26 is greater than the denominator used for estimation. Looking at the answer choices, we see that the closest answer choice is 60%.

So, correct answer is Option D

Step 1 & 2: Understand Question and Draw Inference

Given

First  investment Scheme

• In the first scheme a person invests the amount at simple interest.
• We know, Simple Interest → S.I. =  , where P is the amount invested, P is the rate of interest for the investment, & T is the time during which the investment is made.
• Given to us is T =2 years, R =10% p.a., but we do not know the principal amount of 1 investment scheme (P ) over here.
• Since we do not know the value of P , we will not be able to calculate the amount of simple interest earned under the first investment scheme.

Second  investment Scheme

• In the second investment scheme he invests the amount at the compound interest.
• We know, in investment under compound interest, amount is given by where P₂ is the amount invested, R₂ is the rate of interest for the investment, & n is the time for which the investment is made.
• Given to us is n=2 years, R₂ =10% p.a, but we do not know the principal amount (P₂ ) of 2 investment scheme over here.
• Since we do not know the value of P , we will not be able to calculate the amount earned under the second investment scheme and thus will not be able to calculate the compound interest.
• Also Given is P₁ = P₂ (an equal amount of money is invested in both the schemes)

To Find:

• Difference in the interests earned under two investments scheme i.e. C.I. -S.I
• Since for knowing the values of S.I. and C.I. , we need to know the principal amount under two schemes, we need to analyse the statements further to be able to calculate the difference in the interests under two schemes.

Step 3 : Analyze Statement 1 independent

Statement 1

• The amount the person invests in each scheme is $10,000.
• So we know the Principal amount invested under each scheme or we are given the value of P₁ & P₂ , we will be able to calculate the C.I. and S.I. as already established above.
• Thus statement 1 will be sufficient to answer the question.

Step 4 : Analyze Statement 2 independent

Statement 2: 

• He earns an interest of $1000 in the 1 scheme at the end of 1 year.
• Now the first scheme is an investment made under Simple interest.
• By the formula of S.I., we have , where S.I. =$1000, R → 10% & T=1 year, we will be able to calculate the value of P.
• The P calculated above will be equal to P i.e. the investment under the first scheme, which in turn is also equal to P2.
• Now calculating the values of P & P2, we will be able to calculate the C.I. and S.I. as already established above.
• Thus statement 2 will be sufficient to answer the question.

Step 5: Analyze Both Statements Together (if needed)

• Since from statement 1 and statement 2, we are able to arrive at a unique answer, combining and analysing statements together is not required.
• Hence the correct answer is option D

Step 1 & 2: Understand Question and Draw Inference

Bank A

• Principal invested = x dollars
• Interest rate = y% per annum simple interest
• Time period = n years

Bank B

• Principal invested = x dollars
• Interest rate = z% per annum simple interest
• Time Period = m years

To Find: Is Interest generated in the investment in Bank A > Interest generated in the investment in Bank B?

Step 3 : Analyze Statement 1 independent

1. The amount received at the end of the tenure from bank A was less than twice the amount received from bank B.

However, we cannot say for sure if    Hence insufficient to answer.

Step 4 : Analyze Statement 2 independent

2. Had the rate of simple interest offered by bank B equal to the rate of simple interest offered by Bank A, it would have taken bank B 2m years to generate the same amount of interest as it did in m years with z percent per annum rate of simple interest.

•  As it takes bank B more years to generate the same interest, bank A’s interest is being equated to bank B’s interest.

​

• As bank B will take 2m years to generate the same interest as it generated earlier, we can write

Putting this in (3), the question simplifies to:

However we do not know for sure if n > m. Insufficient to answer.

Step 5: Analyze Both Statements Together (if needed)

Answer : E

Given:

• Amount lent = $2000
• Repayment = 5% of the amount lent every 6 months
  • Repayment amount = 5% of $2000 = $100 every 6 months
• Interest charged = 5% per every 3 months on $2000
  • Interest charged = 5% of $2000 = $100 every 3 months

To Find: Total amount paid to the money lender?

Approach:

1. Total amount paid to the moneylender = Principal Repaid + Interest paid
   • We know Principal Repaid = $2000
2. For finding the total interest paid, we need to find the time period for which the interest was paid
   • Since the rate of interest is given per quarter, we need to express the time period too in terms of quarters.
3. Now, the time period for which the interest was paid is equal to the time for which Repayments of the principal were done.
   • As $100 of the principal was repaid every 6 months (that is, half-year), we can find the number of half-years takentime taken to pay the total principal
     • (Number of half-years)=(Total Principal to be Repaid)/(Repayment done per half-year)
     • So, (Number of quarters taken to complete repayment) = 2(Number of half-years)

Working out:

1. Total principal to be paid = $2000
   • Principal paid every half year = $100
   • So, it will take half years to pay back $2000
2. 20 half years = 40 quarters
   • Interest paid in 1 quarter = $100
   • Interest paid in 40 quarters = 40 * 100 = $4000
3. Total amount paid = $2000 + $4000 = $6000

Hence, Ricky paid a total amount of $6000 to the money lender including the principal and the interest.

Answer : D

Given:

• Let the amount invested, P, be equal to x dollars
• Rate of interest, R = 20% per annum compounded annually
• Time period, n = 2 years
• Interest, CI = $176

 To Find: Value of x?

Approach:

1. We know that Compound Interest,  
   • We will put the values of the different entities in the above equation to calculate the value of x

Working out:

So, the amount invested was $400.

Answer : C

Given:

• Principal = $20,000
• Rate of Interest:
• 1^st year: 10%
• 2^nd year: 20%
• 3^rd year: 5%

To Find: The Amount by which her money grew in 3 years

Approach:

1. Amount by which her money grew = (Amount at the end of 3 year) – (Principal)
   • = (Amount at the end of 3^rd year) – 20,000
2. To calculate the amount at the end of 3^rd year, we will have to consider the successive annual % increases in the invested amount

Working out:

• Remember that we are not asked about the amount at the end of 3^rd year, but about the amount by which her money grew in 3 years
  • Growth in her money = 27,720 - 20,000 = 7,720

So, the correct answer is Option B

Given:

• Amount invested = $1000
• Time period of investment = 17 years
• Rate of interest
  • 0- 2 years = x% p.a. compounded annually
  • 3-7 years = 12% p.a. simple interest
  • 8-17 years = 14% p.a. simple interest
• Total interest earned for the time period 8 – 17 years = $1694 on the amount at the end of the 2 year.

To Find:

By what percentage of the invested amount was the total simple interest earned greater than the compound interest earned?

• Let the total simple interest earned be SI and the total compound interest earned be CI.
• SO, the difference between the interest earned = SI – CI. 
• We need to find the value of 
  • So, we need to find the value of SI – CI or the values of SI and CI

Approach:

1. Total Simple interest earned = $1694 + interest earned from 3-7 years at 12% p.a.
   • We know that Simple interest = 
   • To find the simple interest earned from 3- 7 years we need to know the principal on which the interest rate of 12% p.a. was applied, i.e. the principal at the end of the 2 year.
2. Compound interest earned = Interest earned in 0-2 years at x% p.a.
   • Compound Interest = , where principal Invested = $1000
   • So, to calculate the compound interest, we need to know the final amount at the end of the 2^nd year,
   • Let the amount at the end of 2^nd year be P
3. As we are given that principal P at 14% p.a. simple interest earned a total interest of $1694, we can find the principal P using the formula  

Working out:

1. For the time period 8-17 years

a. Principal = P
b. Rate of Interest = 14% p.a.
c. Time period = 17 - 8 + 1 = 10 years

d.  

2. For the time period 3-7 years
a. Principal = $1210
b. Rate of interest = 12% p.a.
c. Time period = 5 years

3. Total simple interest earned = $1694 + $726 = $2420……..(1)
4. For the time period 0-2 years
a. Principal = $1000
b. Amount = P = $1210
c. Total compound interest earned = $1210 - $1000 = $210…….(2)

Answer : B

Given:

• P = $2000
• Let the rate of return be R% per annum
• Total compound interest earned in 6 years = $4000
• So, Amount after 6 years = Principal $2000 + Interest $4000 = $6000

To Find: Number of Years after which she earned a total interest of $52,000

Approach:

1. Let the total interest be $52,000 after x years of investment
   • So, Amount after x years = Principal $2,000 + Interest $52,000 = $54,000

• From this equation, it’s clear that to find the value of x, we need to find the value of R.

2. We’re given another detail of this investment. In 6 years of time, the principal $2000 had grown to an amount of $6000. Using this, we can find the value of R.

Working out:

• Note: the reason why we stopped at this point and didn’t calculate till the value of R is that the equation in which R is going to be used (see the equation right under the heading ‘Finding the value of x’) contains   only. So, it will
  be a wastage of time if we first solved the above equation till we got the exact value of R, and then, after substituting that
  value of R in the below equation, spent time in calculating the value of 

Substituting the above found value of   in the above  equation:

• Since the base is equal on both sides of the equation, the powers must be equal as well:

• So, x = 18 years

Looking at the answer choices, we see that the correct answer is Option A

Given:

• Case-I
  • Principal , P = $200
    • Rate of interest = x% p.a.
  • Principal, P = $500
    • Rate of Interest = y% p.a.
  • Combined yearly return = 10%
• Case-II
  • Principal, P = $400
    • Rate of interest = x% p.a.
  • Principal, P = $600
    • Rate of Interest = y% p.a.
  • Combined yearly return = 9.2%

To Find: Combined yearly return if $100 each is invested at x% p.a. and y% p.a.?

• Let the combined yearly return be R%
• So, Return on $200 invested at R% p.a. = Return on $100 at x% p.a. + Return on $100 at y% p.a.
• 

Approach:

1. For finding the value of R, we need to find the value of x and y.
2. We are given two cases in which the principals are invested at x% and y% per annum and we are also given the combined yearly return for both the cases
   • The combined yearly return is equal to the sum of the returns of the individual investments
   • Writing the combined yearly return equations for each of the case will give us an equation in x and y
3. We will solve both the equations to get the value of x and y, which will be used to calculate the yearly return on $100 each invested at x% and y% p.a.

Working out:

1. Case-I

• As the combined yearly return is equal to the sum of the returns of individual investments, we can write the following equation
• 
• 2x +5y = 70……………..(1)

2. Case-II

• As the combined yearly return is equal to the sum of the returns of individual investments, we can write the following equation

3. Solving (1) and (2), we have y = 12 and x = 5
4. Hence, combined yearly return on investment of $100 each at x% and y% can be calculated as

Answer : C

Given:

• Scheme A
  • Principal P_A invested = x dollars
  • Rate of interest, R_A = 10% p.a. Simple Interest
  • Investment time, T_A = 2 years
  • Amount received after 2 years = A_A
• Scheme B
  • Principal P_B invested = x dollars
  • Rate of interest, R_B = 10% p.a. compounded annually
  • Investment time, T_B = 2 years
  • Amount received = A_B
• A_B - A_A = 63
   

To Find: Value of x?

Approach:

• For finding the value of x, we need to form an equation in x.
• As we are given that x dollars each was invested in schemes A and B, we
• can calculate the amount received from schemes A and B using the following formula:

3. We can then use the relation A_B- A_A = 63 to formulate an equation in x.

Working out:

3. Substituting the values of A and A in the relation A - A = 63, we have
a. 1.21x - 1.20x = 63
b x = $6300

Hence, Pedro invested $6300 in scheme A

Answer : D

Given:

• Scheme A
  • Principal invested = $5000
  • Time period = 4 years
  • Offered a fixed rate of return
• Scheme B
  • Each year investment = Interest generated from scheme A in
  • pervious year
  • Rate of interest in 4 year = 5% p.a.
• Total Interest generated
  • Year 1 = $500
  • Year 2 = $550
  • Year 3 = $710

To Find: Total interest earned in the 4 year from both the schemes?

Approach:

1. For finding the total interest earned in the 4 year, we need to find the interest earned from both the schemes.
2. For finding the interest earned, we need to find the principal and the rate of interest of both the schemes.
3. Scheme A
   • As the interest generated in every year is taken out, the principal in scheme A will not change. So, the principal in scheme A in 4 year = $5000
   • As scheme A offers, a fixed rate of return every year, if we can find the rate of interest in any one of the year, we will be able to find the rate of interest offered in the 4^th year
   • In the 1^st year, the total interested generated will be equal to the interest generated by scheme A. As we know the principal and the interest generated for the 1^st year, we can find the rate of interest offered by scheme A
4. Scheme B
   • As we are given the interest rate offered by scheme B in the 4^th year, we only need to find the principal.
   • (The principal of scheme B in the 4^th year) = (The interest generated by scheme A in the 1^st + 2^nd +3^rd year) + (The interest generated in scheme B in the 2^nd and the 3^rd year)
   • As we already know the interest generated by scheme A in each year(which is constant), we can find the sum of the interest generated by scheme A in 3 years.
   • Also, since we are given the total interest generated by the schemes in the 1^st , 2^nd and the 3^rd year, we can find the interest generated by scheme B in each year

Working out:

1. Interest generated by scheme A = $500 each year
   • Since the interest generated in the 1 year will exclusively come from scheme A
2. As scheme A generates a fixed interest every year, it will generate an interest of $500 every year
3. Also, as $500 was received as interest in year 1, the rate of interest for 

4. Principal of scheme B will grow each year by the interest generated in scheme A as well as the interest generated in scheme B

• Hence, the principal of scheme B at the start of the 4 year = 500 * 3 + 50 + 210 = 1760

5. So, the interest generated in 4 year:
a. Scheme A = $500
b. Scheme B = 5% of 1760 = $88
c. Total interest = 500 + 88 = $588

Answer : C