James invested $100,000 in fund A at the beginning of 2012. The fund made losses during the year and he suffered a loss of 20 percent. At the beginning of 2013, he took his remaining money out of fund A and invested it in fund B. Fund B gave him an annual rate of 20 percent in 2013 and 10 percent in 2014. If he did not take out the interest earned from fund B in 2013, by what percent did his money grow from the beginning of 2012 to the end of 2014?
Given:
Fund A - 2012
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
At the start of 2015, Jane opened two new accounts – X and Y – to invest her total savings of $1000. She invested p percent of her savings in account X, which yielded a simple interest of 8 percent per annum, and the rest of the savings in account Y, which yielded a simple interest of 6 percent per annum. Was the amount of interest earned by account X greater than the amount of interest earned by account Y during the year 2015?
(1) The value of p was between 25 and 30, inclusive
(2) The total interest earned by the two accounts during 2015 was $66
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’
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’
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
An investment of $200,000 in an instrument that returns an annual rate of r percent compounded semi-annually grows to $220,500 in
one year. What is the value of r?
Given:
= 2 half- years (that is, 2 periods of compounding)
To Find: r = ?
Approach:
Working out:
Lucy deposited $62500 in an investment fund that provided 16 percent annual return compounded quarterly. If she made no other transactions with the fund, in how much time, in months, did her investment earn a total interest of $5100?
Given:
To Find: Time Period of Investment in Months
Approach:
Working out:
If $200,000 invested at r percent per year, compounded quarterly, grow by $88,000 in 6 months, what is the value of r?
Given:
To Find: r = ?
Approach:
Working out:
So, r = 80%
Looking at the answer choices, we see that the correct answer is Option E
Dan borrows a sum of $10,000 from Lucy. Lucy charges Dan an interest of 10% p.a. compound interest, compounded annually. If
Dan pays back a total of $13310 to Lucy, after how many years Dan pays back his entire debt?
Given:
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:
Working out:
Comparing both sides of the equation (as both are raised to sake base
we get
n=3 years.
Answer
Jane and Nancy each saved $2000 in the year 2014. If Jane saved 10% more in year 2015 than in year 2014, and Nancy saves 15%
less than what Jane saves in the year 2015, how much less money does Nancy save in year 2015 than in year 2014?
Given:
_{}To Find:
Approach:
Working out:
Answer :
Roger distributed a total investment of $1000 between mutual funds A and B and received a combined yearly return of 10 percent. How much did he invest in mutual fund A?
(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
(2) He received a return of 8 percent from mutual fund B
Step 1 & 2: Understand Question and Draw Inference
Given:
To find :a = ?
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
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)
So, even after both statements together, we cannot find a unique value of a.
Answer: Option E
In the first year of a couple's marriage, the wife’s earnings were 40 percent of the combined earnings of the couple. The wife invested 40 percent of her earnings at an annual return of 5 percent and the husband invested 30 percent of his earnings at an annual return of 10 percent. In the second year of their marriage, the combined earnings of the couple increased by 10 percent and the wife’s earnings were five-sixths of her husband’s earnings. The wife invested 48 percent of her earnings and the husband invested 50 percent of his earnings in their respective investment instruments of the previous year. If the couple made no other investments and took out the interest earned in the first year at the beginning of the second year, by approximately what percent was the interest earned by the couple in the second year greater than the interest earned by the couple in the first year of their marriage? The interest income from the couple’s investments is not considered in their earnings.
Given:
To Find: Approximate percentage by which the 2^{nd} year interest is greater than the 1^{st} year interest
Approach:
Working out:
So, correct answer is Option D
A person invests an equal amount of money in two investment schemes for two years. In the first investment scheme, he earns an
interest at 10% p.a. simple interest and in the second investment scheme he earns an interest at 10% p.a. compounded annually.
What is the difference in the interest earned under the two investment schemes at the end of the second year?
Step 1 & 2: Understand Question and Draw Inference
Given
First investment Scheme
Second investment Scheme
To Find:
Step 3 : Analyze Statement 1 independent
Statement 1
Step 4 : Analyze Statement 2 independent
Statement 2:
Step 5: Analyze Both Statements Together (if needed)
Rosy invested x dollars at a simple interest of y percent per annum for n years with bank A and x/2 dollars at a simple interest of z percent per annum for m years with bank B. Was the interest generated at the end of the respective tenures of investments greater in bank A than in bank B?
1) The amount received at the end of the tenure from bank A was less than twice the amount received from bank B.
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.
Step 1 & 2: Understand Question and Draw Inference
Bank A
Bank B
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
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.
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
A moneylender lent $2000 to Ricky with the condition that Ricky will pay back 5 percent of this amount every half year. Till Ricky repaid the original loan amount (principal) completely, the moneylender charged an interest equal to 5 percent per quarter on the original loan amount. Ricky always made interest payments and principal repayments on time. (For example, at the end of the first quarter, Ricky paid the moneylender 5 percent of $2000 as interest and at the end of 6 months, Ricky paid the money lender 5 percent of $2000 as interest and 5 percent of $2000 as principal repayment). What was the total amount in dollars that Ricky paid to the moneylender?
Given:
To Find: Total amount paid to the money lender?
Approach:
Working out:
Hence, Ricky paid a total amount of $6000 to the money lender including the principal and the interest.
Answer : D
What dollar amount invested at the rate of 20 percent per annum compounded annually for 2 years yields an interest of $176?
Given:
To Find: Value of x?
Approach:
Working out:
So, the amount invested was $400.
Answer : C
Sonya invested $20,000 in a mutual fund scheme, which calculated and reinvested the interest earned in the scheme annually. She received a return of 10 percent in the first year, 20 percent in the second year and 5 percent in the third year. By what amount, in dollars, did her money grow in the three years?
Given:
To Find: The Amount by which her money grew in 3 years
Approach:
Working out:
So, the correct answer is Option B
Martina invested $1000 for a period of 17 years in a bank that paid variable rates of interest. For the first 2 years, the bank paid an annual interest rate of x percent compounded annually and for the next 5 years, the bank paid a simple interest rate of 12 percent per annum on the compounded amount at the end of the second year. If for the remaining years, Martina earned a total simple interest of $1694 on the compounded amount at the end of the second year, at a rate of 14 percent per annum, by approximately what percentage of the invested amount was the total simple interest earned greater than the compound interest earned?
Given:
To Find:
By what percentage of the invested amount was the total simple interest earned greater than the compound interest earned?
Approach:
Working out:
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
Roxie invested $2000 in an account that yielded a fixed rate of annual return compounded annually throughout the duration of
investment. If she earned a total interest of $4000 in 6 years, after how many years of investment did she earn a total interest of
$52000?
Given:
To Find: Number of Years after which she earned a total interest of $52,000
Approach:
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:
Substituting the above found value of in the above equation:
Looking at the answer choices, we see that the correct answer is Option A
A $200 investment at x percent per annum and a $500 investment at y percent per annum have a combined yearly return of 10 percent of the total of the two investments. If $400 is invested at x percent and $600 is invested at y percent per annum to give a combined yearly return of 9.2 percent of the total of the two investments, what will be the combined percentage yearly return of the total investment if $100 each is invested at x percent per annum and y percent per annum respectively?
Given:
To Find: Combined yearly return if $100 each is invested at x% p.a. and y% p.a.?
Approach:
Working out:
2. Case-II
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
Petro invested x dollars each in scheme A and scheme B for two years. Scheme A offered a simple interest rate of 10 percent per
annum while scheme B offered an interest rate of 10 percent per annum compounded annually. If the amount received by Petro at
the end of two years in scheme B was $63 greater than the amount received from scheme A, how much in dollars did he invest in
scheme A?
Given:
To Find: Value of x?
Approach:
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
Novak invested $5000 in scheme A for 4 years, which gave a fixed rate of return each year. From the second year of this investment, the interest earned on scheme A in the previous year was reinvested annually in scheme B, whose annual rate of interest, compounded annually, varied with the performance of scheme B in that particular year. If the total interest earned from both the schemes in the first 3 years was $500, $550 and $710 respectively and scheme B offered an interest rate of 5 percent per annum in the fourth year, what was the total interest in dollars that was earned in the fourth year from both the schemes?
Given:
To Find: Total interest earned in the 4 year from both the schemes?
Approach:
Working out:
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
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
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