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Test: Simple And Compound Interest Including Annuity - 2 - CA Foundation MCQ


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30 Questions MCQ Test Quantitative Aptitude for CA Foundation - Test: Simple And Compound Interest Including Annuity - 2

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Test: Simple And Compound Interest Including Annuity - 2 - Question 1

 If a sum triples in 15 years at simple rate of interest, the rate of interest per annum will be: 

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 2 - Question 1

Given Data:
The sum triples in 15 years, meaning A = 3P.
Time (T) = 15 years.
Formula for Simple Interest:
A = P(1 + (R × T) / 100)

Step 1: Substitute the Values
Using the formula:
3P = P(1 + (R × 15) / 100)

Cancel P on both sides:

3 = 1 + (15R / 100)

Step 2: Simplify the Equation
3 - 1 = 15R / 100

2 = 15R / 100

Step 3: Solve for R
R = (2 × 100) / 15

R = 200 / 15 = 13.33%

The rate of interest per annum is 13.3%.

Test: Simple And Compound Interest Including Annuity - 2 - Question 2

How much amount is required to be invested every year as to accumulate Rs.6,00,000 at the end of 10 years, if interest is compounded annually at 10% rate of interest 
[Given: (1.1)10 = 2.59374.]

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 2 - Question 2

Formula to Use

The formula to calculate the Future Value of an Ordinary Annuity (payments made at the end of each period) is:  

FV = A × ((1 + r)ⁿ - 1) / r  

Where:  
- FV = Future Value  
- A = Annual Investment  
- r = Annual Interest Rate (in decimal)  
- n = Number of Years  

Step-by-Step Solution  

1. Plug in the Known Values into the Formula  
6,00,000 = A × ((1 + 0.10)¹⁰ - 1) / 0.10  

2. Calculate (1 + r)ⁿ  
Given:  
(1.1)¹⁰ = 2.59374  

3. Subtract 1 from the Result  
2.59374 - 1 = 1.59374  

4. Divide by the Interest Rate r  
1.59374 / 0.10 = 15.9374  

5. Rearrange the Formula to Solve for A  
A = FV / ((1 + r)ⁿ - 1) / r  
A = 6,00,000 / 15.9374 ≈ 37,647  
 

Test: Simple And Compound Interest Including Annuity - 2 - Question 3

A sum of money compounded annually becomes Rs1,140 in two years and Rs.1,710 in three years. Find the rate of interest per annum. 

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 2 - Question 3



Test: Simple And Compound Interest Including Annuity - 2 - Question 4

The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is:

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 2 - Question 4

Test: Simple And Compound Interest Including Annuity - 2 - Question 5

The S.I. on a sum of money is 4/9 of the principle and the no. of year is equal to the rate of interest per annum. Find the rate of interest per annum?

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 2 - Question 5

Test: Simple And Compound Interest Including Annuity - 2 - Question 6

How much investment is required to yield an Annual income of Rs.420 at 7% p.a. Simple interest.

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 2 - Question 6

Test: Simple And Compound Interest Including Annuity - 2 - Question 7

The difference between compound and simple interest on a certain sum of money for 2 years at 4% is Rs.1. The sum (in Rs) is: 

Test: Simple And Compound Interest Including Annuity - 2 - Question 8

The partners A and B together lent Rs.3,903 at 4% per annum interest compound annually. After a span of 3 years, A gets the same amount as B gets after 9 years. The share of A in the sum of Rs.3,903 would have been: 

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 2 - Question 8

Given:

  • Total sum lent by A and B = Rs. 3,903

  • Interest rate = 4% per annum, compounded annually

  • A gets the same amount after 3 years as B gets after 9 years

Let’s assume:

  • A's share = Rs. x

  • So, B's share = Rs. (3903 − x)

Step 1: Write the amount formulas

Amount received by A after 3 years:
A3 = x × (1 + 0.04)³ = x × (1.04)³

Amount received by B after 9 years:
B9 = (3903 − x) × (1 + 0.04)⁹ = (3903 − x) × (1.04)⁹

Step 2: Set the amounts equal (as given in question)

x × (1.04)³ = (3903 − x) × (1.04)⁹

Divide both sides by (1.04)³:

x = (3903 − x) × (1.04)⁶

Substitute (1.04)⁶ = 1.265319:

x = (3903 − x) × 1.265319

x = 3903 × 1.265319 − x × 1.265319

x + x × 1.265319 = 3903 × 1.265319

x × (1 + 1.265319) = 3903 × 1.265319

x × 2.265319 = 4941.97

x = 4941.97 ÷ 2.265319

x ≈ 2182

Final Answer:
The share of A in the sum of Rs. 3,903 would have been Rs. 2,182.

Test: Simple And Compound Interest Including Annuity - 2 - Question 9

If the Simple Interest on Rs.1,400 for 3 years is less than the simple interest on Rs.1,800 for the same period by Rs.80, then the rate of interest is 

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 2 - Question 9

Step 1: Use the Simple Interest Formula

Simple Interest (SI) = (P × R × T) ÷ 100

We are given that the difference in SI is Rs. 80. So:

SI on P2 - SI on P1 = 80

Substitute the formula:

(P2 × R × T) ÷ 100 - (P1 × R × T) ÷ 100 = 80

Step 2: Plug in the Given Values

(1800 × R × 3) ÷ 100 - (1400 × R × 3) ÷ 100 = 80

Simplify both terms:

(5400R ÷ 100) - (4200R ÷ 100) = 80

Multiply out:

54R - 42R = 80

Step 3: Solve for R (Rate)

12R = 80

Divide both sides by 12:

R = 80 ÷ 12

R = 6.666...%

Rounded to two decimal places:

R = 6.67%

Final Answer:

The rate of interest is 6.67%.

Conclusion:

The correct option is (b) 6.67%.

Answer: (b) 6.67%

Test: Simple And Compound Interest Including Annuity - 2 - Question 10

 In what time will a sum of money double its y at 6.25% p.a. simple interest?

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 2 - Question 10

To find out how long it takes for a sum of money to double at 6.25% per annum with simple interest, follow these steps:

  • Simple interest is calculated using the formula: Interest = Principal × Rate × Time.
  • To double the money, the interest must equal the principal amount.
  • Set up the equation: Principal = Principal × 6.25/100 × Time.
  • Cancel out the principal from both sides: 1 = (6.25/100) × Time.
  • Solve for time: Time = 100/6.25.
  • This results in: Time = 16 years.

Therefore, it will take 16 years for the money to double at 6.25% simple interest.

Test: Simple And Compound Interest Including Annuity - 2 - Question 11

 Simple interest on Rs.2,000 for 5 months at 16% p.a. is__________.

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 2 - Question 11

Here's the calculation:

  • Principal (P) = Rs. 2000
  • Rate of interest (R) = 16% per annum
  • Time (T) = 5 months = 5/12 years

Simple Interest (SI) = (P * R * T) / 100 = (2000 * 16 * 5) / (100 * 12) = Rs. 133.33

Test: Simple And Compound Interest Including Annuity - 2 - Question 12

What principle will amount to Rs.370 in 6 years at 8% p.a. at simple interest?

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 2 - Question 12

Step 1: Use the Simple Interest Formula

The formula is:
A = P + SI

And,
SI = (P × R × T) ÷ 100

So the full formula becomes:
A = P + (P × R × T) ÷ 100

Or,
A = P × (1 + (R × T) ÷ 100)

Step 2: Plug in the Given Values

Given:

  • Amount (A) = 370

  • Rate (R) = 8%

  • Time (T) = 6 years

  • Principal (P) = ? (we have to find this)

Now substitute:

370 = P × (1 + (8 × 6) ÷ 100)

Step 3: Simplify

First calculate 8 × 6 = 48, then divide by 100:

48 ÷ 100 = 0.48

Now add 1:

1 + 0.48 = 1.48

So the equation is:

370 = P × 1.48

Step 4: Solve for P

Divide both sides by 1.48:

P = 370 ÷ 1.48

P = 250

Final Answer:

The required principal is Rs. 250.

Conclusion:

The correct option is (b) Rs. 250.

Answer: (b) Rs. 250

Test: Simple And Compound Interest Including Annuity - 2 - Question 13

On what sum difference between compound interest and simple interest for two years at 7% p.a. interest is Rs.29.4

Test: Simple And Compound Interest Including Annuity - 2 - Question 14

 Mr. X invests Rs.90,500 in post office at 7.5% p.a. simple interest. While calculating the rate was wrongly taken as 5.7% p.a.The difference in amounts at maturity is Rs.9,774. Find the period for which the sum was invested

Test: Simple And Compound Interest Including Annuity - 2 - Question 15

A sinking fund is created for redeming debentures worth Rs. 5 lakhs at the end of 25 years. How much provision needs to be made out of profits each year provided sinking fund investments can earn interest at 4% p.a.?

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 2 - Question 15

Test: Simple And Compound Interest Including Annuity - 2 - Question 16

 A machine costs Rs. 520000 with an estimated life of 25 years. A sinking fund is created to replace it by a new model at 25% higher cost after 25 years with a scrap value realization of Rs. 25000. What amount should be set aside every year if the sinking fund investments accumulate at 3.5% compound interest p.a.?

Test: Simple And Compound Interest Including Annuity - 2 - Question 17

Johnson left Rs. 100000 with the direction that it should be divided in such a way that his minor sons Tom, Dick and Harry aged 9, 12 and 15 years should each receive equally after attaining the age 25 years. The rate of interest being 3.5%, how much each son receive after getting 25 yeas old?

Test: Simple And Compound Interest Including Annuity - 2 - Question 18

A machine worth Rs. 490740 is depreciated at 15% on its opening value each year. When its value would reduce to Rs. 200000?

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 2 - Question 18

 

Given

  • Initial value of the machine = Rs. 490740
  • Depreciation rate = 15% per annum on opening value
  • Final value = Rs. 200000

We need to find the time (in years and months) it takes for the value to reduce to or just below Rs. 200000.

Step-by-step:

This is exponential depreciation, so we use the formula:

V = P(1 - r)^t

Where:

  • V = 200000 (final value)
  • P = 490740 (initial value)
  • r = 0.15 (15%)
  • t = time in years

Substitute into the formula:

200000 = 490740 × (0.85)^t
200000 / 490740 ≈ (0.85)^t
0.4076 ≈ (0.85)^t
  

Taking logarithm on both sides:

log(0.4076) = t × log(0.85)
t = log(0.4076) / log(0.85)
t ≈ -0.3894 / -0.0706 ≈ 5.51 years
  

Convert decimal to years and months:

0.51 × 12 ≈ 6.12 months
So, t ≈ 5 years 6 months
  

Correct answer: d) 5 years 7 months (approx.) ✅

(Since depreciation occurs in full months/years, we round to the nearest month.)

Test: Simple And Compound Interest Including Annuity - 2 - Question 19

A machine depreciates at 10% of its value at the beginning of a year. The cost and scrap value realized at the time of sale being Rs. 23240 and Rs. 9000 respectively. For how many years the machine was put to use?

Test: Simple And Compound Interest Including Annuity - 2 - Question 20

In how many years will a sum of money double at 5% p.a. compound interest?

Test: Simple And Compound Interest Including Annuity - 2 - Question 21

 In how many years a sum of money trebles at 5% p.a. compound interest payable on half yearly basis?

Test: Simple And Compound Interest Including Annuity - 2 - Question 22

A machine worth Rs. 490740 is depreciated at 15% of its opening value each year. When its value would reduce by 90?

Test: Simple And Compound Interest Including Annuity - 2 - Question 23

 If the difference of S.I. and C.I. is Rs. 72 at 12% for 2 years. Calculate the amount.

Test: Simple And Compound Interest Including Annuity - 2 - Question 24

 If a simple interest on a sum of money at 6% p.a.for 7 years is equal to twice of simple interest on another sum for 9 years at 5% p.a.. The ratio will be:

Test: Simple And Compound Interest Including Annuity - 2 - Question 25

Appu retires at 60 years receiving a pension of 14400 a year paid in half-yearly installments for rest of his life after reckoning his life expectation to be 13 years and that interest at 4% p.a. is payable half-yearly. What single sum is equivalent to his pension?

Test: Simple And Compound Interest Including Annuity - 2 - Question 26

Raja aged 40 wishes his wife Rani to have Rs. 40 lakhs at his death. If his expectation of life is another 30 years and he starts making equal annual investments commencing now at 3% compound interest p.a. how much should he invest annually?

Test: Simple And Compound Interest Including Annuity - 2 - Question 27

The present value of Rs. 10000 due in 2 years at 5% p.a. compound interest when the interest is paid on yearly basis is Rs. ________.

Test: Simple And Compound Interest Including Annuity - 2 - Question 28

 Alibaba borrows R.s 6 lakhs Housing Loan at 6% repayable in 20 annual installments commencing at the end of the first year. How much annual payment is necessary. 

Test: Simple And Compound Interest Including Annuity - 2 - Question 29

The present value of Rs. 10000 due in 2 years at 5% p.a. compound interest when the interest is paid on half-yearly basis is Rs. __________.

Test: Simple And Compound Interest Including Annuity - 2 - Question 30

If A=Rs. 10000, n=18 yrs., R=4% p.a. C.I, P will be

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