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Test: Simple And Compound Interest Including Annuity - 1 - CA Foundation MCQ


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30 Questions MCQ Test - Test: Simple And Compound Interest Including Annuity - 1

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

Choose the most appropriate option (a) (b) (c) (d)

S.I on Rs. 3500 for 3 years at 12% per annum is

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

The formula for Simple Interest (SI) is: SI = (P x R x T) / 100

Where, P = Principal amount (Rs. 3500) R = Rate of interest (12%) T = Time (3 years)

So, SI = (3500 x 12 x 3) / 100 = 1260

Therefore, the simple interest on Rs. 3500 for 3 years at 12% per annum is Rs. 1260. So the answer is 2. Rs. 1260

 

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

P = 5000, R = 15, T = 4 ½ using I = PRT/100, I will be

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

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Test: Simple And Compound Interest Including Annuity - 1 - Question 3

If P = 5000, T = 1, I = Rs. 300, R will be

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 1 - Question 3

Test: Simple And Compound Interest Including Annuity - 1 - Question 4

 Find the compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually.

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 1 - Question 4

Test: Simple And Compound Interest Including Annuity - 1 - Question 5

P = Rs. 12000, A = Rs. 16500, T = 2 ½ years. Rate percent per annum simple interest will be P = Rs. 12000.

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 1 - Question 5

Calculation of Rate Percent per Annum

- Given:
- Principal amount (P) = Rs. 12000
- Amount (A) = Rs. 16500
- Time (T) = 2 ½ years

- We know that:
- Simple Interest (SI) = A - P
- SI = P * R * T / 100

- Substituting the given values:
- A - P = P * R * T / 100
- 16500 - 12000 = 12000 * R * 2.5 / 100
- 4500 = 300 * R
- R = 4500 / 300
- R = 15%

Therefore, the rate percent per annum is 15%, which corresponds to option A.

Test: Simple And Compound Interest Including Annuity - 1 - Question 6

P = Rs. 10000, I = Rs. 2500, R = 12 ½% SI. The number of years T will be

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 1 - Question 6

Test: Simple And Compound Interest Including Annuity - 1 - Question 7

P = Rs. 8500, A = Rs. 10200, R = 12 ½ % SI, t will be.

Test: Simple And Compound Interest Including Annuity - 1 - Question 8

The sum required to earn a monthly interest of Rs 1200 at 18% per annum SI is

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 1 - Question 8

Test: Simple And Compound Interest Including Annuity - 1 - Question 9

In simple interest, a sum of money amounts to ₹ 6,200 in 2 years and ₹ 6,800 in 3 years. Find the principal and rate of interest.

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 1 - Question 9

Let the principal be P and the rate of interest be R%.
Using the simple interest formula: Amount = Principal + (Principal × Rate × Time) / 100
For 2 years: 6,200 = P + (P × R × 2) / 100 6,200 = P(1 + 2R/100)  ... (1)
For 3 years: 6,800 = P + (P × R × 3) / 100 6,800 = P(1 + 3R/100)  ... (2)
Subtract equation (1) from equation (2):
6,800 - 6,200 = P[(1 + 3R/100) - (1 + 2R/100)] 600 = P(R/100) P = 600 × 100 / R P = 60,000 / R  ... (3)
Substitute P from equation (3) into equation (1):
6,200 = (60,000 / R)(1 + 2R/100) 6,200
=(60,000 / R) + 1,200 6,200 - 1,200
= 60,000 / R 5,000
= 60,000 / R
R = 60,000 / 5,000
R = 12% Now, substitute R back into equation (3):
P = 60,000 / 12 P = 5,000 The principal is ₹5,000 and the rate of interest is 12%. 

Test: Simple And Compound Interest Including Annuity - 1 - Question 10

A sum of money doubles itself in 10 years. The number of years it would triple itself is

Test: Simple And Compound Interest Including Annuity - 1 - Question 11

If P = Rs. 1000, R = 5% p.a, n = 4; Amount and C.I. is

Test: Simple And Compound Interest Including Annuity - 1 - Question 12

Rs. 100 will become after 20 years at 5% p.a compound interest calculated annually

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 1 - Question 12

⇒ Hence, r = 5/100 = 0.05.

⇒ So, A = 100(1 + 0.05/1)^(1×20).

⇒ This yields A = 100(1 + 0.05)^20 = 100(1.05)^20.

⇒ This comes out to A =~ Rs. 265.33.

Therefore, Rs. 100 will become approximately Rs. 265.33 after 20 years at 5% per annum compound interest.

Hence, the correct answer is approximately 265.50.

Test: Simple And Compound Interest Including Annuity - 1 - Question 13

The effective rate of interest corresponding to a nominal rate 3% p.a payable half yearly is

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 1 - Question 13

The amount after 1 year at 8% per annum when interest is compounded half yearly is

=100(1+3/2/100)2×1=100(101.5/100)2=103.0225
CI for 1 year = 103.0225 – 100 = 3.0225
The effective annual rate of interest is = 3.0225%

Test: Simple And Compound Interest Including Annuity - 1 - Question 14

A machine is depreciated at the rate of 20% on reducing balance. The original cost of the machine was Rs. 100000 and its ultimate scrap value was Rs. 30000. The effective life of the machine is

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 1 - Question 14

Cost of machine (P) = Rs 1,00,000

Scrap value (A) = Rs 30,000

Rate of Depreciation = 20% per annum on reducing value

The effective life of the machine in years is the number of years in which P (Rs 1,00,000) would reduce to A (scrap value Rs 30,000) reducing at the rate of 20% per annum of the value at the start of that year year.

Value of the machine at time t= 0 years = P

The depreciated cost at end of one year = P[1 — 20%] = P[1 — 0.2] = P × 0.8

At the end of second year = P × 0.8²

At the end of 3rd year = P × 0.8³

And so on.

Let after n years the value depreciate to scrap value. We are required to find n.

P(0.8)^n = A

1,00000 (0.8)^n = 30,000

=> (0.8)^n = (30,000)/(1,00,000) = 0.3

Taking log of both sides

n log (0.8) = log (0.3)

=>n × (-0.09691) = (-0.52288)

=> n = (-0.52288)/(-0.09691)= 5.396 year ~5.4 years

Test: Simple And Compound Interest Including Annuity - 1 - Question 15

If A = Rs. 1000, n = 2 years, R = 6% p.a compound interest payable half-yearly, then principal (P) is

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 1 - Question 15

Test: Simple And Compound Interest Including Annuity - 1 - Question 16

The population of a town increases every year by 2% of the population at the beginning of that year. The number of years by which the total increase of population be 40% is

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 1 - Question 16

To determine the number of years it takes for the population to increase by 40% given a 2% annual increase, we can use the compound interest formula:

Thus, the number of years it takes for the population to increase by 40% is approximately 17 years.

Test: Simple And Compound Interest Including Annuity - 1 - Question 17

The difference between C.I and S.I on a certain sum of money invested for 3 years at 6% p.a is Rs. 110.16. the sum is

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 1 - Question 17

Let the principal be P. The rate of interest is 6% per annum, and the time period is 3 years.

So, the sum of money is Rs. 10,000.

Test: Simple And Compound Interest Including Annuity - 1 - Question 18

The useful life of a machine is estimated to be 10 years and cost Rs.10,000. Rate of depreciation is 10% p.a. The scrap value at the end of its life is

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 1 - Question 18

Test: Simple And Compound Interest Including Annuity - 1 - Question 19

The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 1 - Question 19
  • The nominal interest rate is 6% per annum, compounded half-yearly.
  • This means the interest is applied twice a year at a rate of 3% (6% / 2).
  • To find the effective annual rate (EAR), use the formula: EAR = (1 + r/n)^(nt) - 1, where r is the nominal rate, n is the number of compounding periods per year, and t is the number of years.
  • Plugging in the values: EAR = (1 + 0.03)^2 - 1 = 0.0609 or 6.09%.
Test: Simple And Compound Interest Including Annuity - 1 - Question 20

The C.I on Rs. 16000 for 1 ½ years at 10% p.a payable half -yearly is

Test: Simple And Compound Interest Including Annuity - 1 - Question 21

The C.I on Rs. 40000 at 10% p.a for 1 year when the interest is payable quarterly is

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 1 - Question 21

Test: Simple And Compound Interest Including Annuity - 1 - Question 22

The difference between the S.I and the C.I on Rs. 2400 for 2 years at 5% p.a is

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 1 - Question 22

Test: Simple And Compound Interest Including Annuity - 1 - Question 23

The annual birth and death rates per 1000 are 39.4 and 19.4 respectively. The number of years in which the population will be doubled assuming there is no immigration or emigration is

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 1 - Question 23

Given: b( birth rate)=39.4/1000, d(death rate) =19.4/1000

b-d= 39.4–19.4=20/1000 i.e.0.02

P( population) = 2P( population)

To find: t=?

Solution :Let's assume P=1000

applying formula:

An= p(1+i)n

Putting values:

2000=1000(1+0.02)n

2=1.02n

n=35 years.

Test: Simple And Compound Interest Including Annuity - 1 - Question 24

The C.I on Rs. 4000 for 6 months at 12% p.a payable quarterly is

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 1 - Question 24

Calculation of Compound Interest
 


  • Principal amount (P) = Rs. 4000

  • Rate of interest (R) = 12% per annum

  • Time period (T) = 6 months = 0.5 years

  • Interest compounded quarterly, so n = 4

  • Using the formula for compound interest: A = P(1 + R/n)^(nt)

  • Substitute the values: A = 4000(1 + 0.12/4)^(4*0.5)

  • Calculating further, A = 4000(1 + 0.03)^2

  • A = 4000(1.03)^2 = 4000(1.0609) = Rs. 4243.60

  • Compound Interest (CI) = A - P = 4243.60 - 4000 = Rs. 243.60


  •  



Therefore, the compound interest on Rs. 4000 for 6 months at 12% per annum payable quarterly is Rs. 243.60. So, option A is the correct answer.

Test: Simple And Compound Interest Including Annuity - 1 - Question 25

The present value of an annuity of Rs. 3000 for 15 years at 4.5% p.a CI is

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 1 - Question 25

Test: Simple And Compound Interest Including Annuity - 1 - Question 26

The amount of an annuity certain of Rs. 150 for 12 years at 3.5% p.a C.I is

Test: Simple And Compound Interest Including Annuity - 1 - Question 27

A loan of Rs. 10.000 is to be paid back in 30 equal instalments. The amount of each installment to cover the principal and at 4% p.a CI is

Test: Simple And Compound Interest Including Annuity - 1 - Question 28

A = Rs. 1200 n = 12 yrs i = 0.08 v = ?

Test: Simple And Compound Interest Including Annuity - 1 - Question 29

a = Rs. 100 n = 10 i = 5% find the FV of annuity

Using the formula FV = a / {1 + i) n – 1}, M is equal to

Test: Simple And Compound Interest Including Annuity - 1 - Question 30

If the amount of an annuity after 25 years at 5% p.a C.I is Rs. 50000 the annuity will be

Detailed Solution for Test: Simple And Compound Interest Including Annuity - 1 - Question 30

Given:

  • Future value (amount accumulated): Rs. 50,000
  • Interest rate (compound interest rate): 5% per annum (0.05 in decimal)
  • Number of years (periods): 25 years

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