Compound Interest MCQ Quiz - Objective Question with Answer for Compound Interest - Download Free PDF

Given:

Principal (P) = ₹10000

Time (t) = 2 years

CI at rate (x + 6)% = ₹3456

Formula used:

Amount A = P

CI = A - P

Calculations:

Let r = x + 6

⇒ 10000 × (1 + r/100)² = 10000 + 3456 = 13456

⇒ (1 + r/100)² = 13456 ÷ 10000 = 1.3456

⇒ √1.3456 = 1 + r/100

⇒ 1.16 = 1 + r/100

⇒ r = 0.16 × 100 = 16 ⇒ x + 6 = 16 ⇒ x = 10

Now, new rate = x + 10 = 20%

CI = 10000 × (1 + 20/100)² - 10000

⇒ CI = 10000 × (1.2)² - 10000

⇒ CI = 10000 × 1.44 - 10000 = 14400 - 10000 = ₹4400

∴ Compound interest at (x + 10)% rate is ₹4400.

Given:

Down payment = Rs. 10,000

Two equal annual installments = Rs. 12,100 each

Interest rate = 10% per annum, compounded yearly

Calculation:

Present value (PV) of the first installment (due after 1 year):

⇒ PV = 12100 ÷ (1 + 10/100) = 12100 ÷ 1.10 = Rs. 11000

Present value (PV) of the second installment (due after 2 years):

⇒ PV = 12100 ÷ (1.10 × 1.10) = 12100 ÷ 1.21 = Rs. 10000

Total cash value of the motorcycle:

⇒ Cash value = Down payment + PV of 1st installment + PV of 2nd installment

⇒ Cash value = 10000 + 11000 + 10000 = Rs. 31,000

Thus, the correct answer is Rs. 31,000.

Principal (P) = Rs. 12000

Simple interest (SI) for 2 years = Rs. 12000

Find compound interest (CI) for 3 years

Concept: Rate of interest can be calculated from SI, then applied to calculate CI.

Solution:

Rate of interest (r) = (SI × 100)/(P × t) = (12000 × 100)/(12000 × 2) = 50% per annum

CI for 3 years at 50% per annum = P[(1 + r/100)3 - 1] = 12000[(1 + 50/100)3 - 1]

CI = 12000[(3/2)3 - 1] = 12000[27/8 - 1] = Rs. 28500

Alternate MethodInterest = 12000 for 2 years

So 

Interest = 6000 for 1 year

Principal = Rs. 12000

Means Rate of Interest = 50%

So

Compound interest for 3 years:-

Compound interest for 2 years = 50 + 50 + 50 × 50/100 = 125%

Compound interest for 3 years = 125 + 50 + 125 × 50/100 = 237.5% of Principal

Compound interest = 237.5 × 12000/100 = 28500

Hence, the compound interest for the first 3 years is Rs. 28500 

GIVEN:

Amount = Rs. 13310,

Rate = 10% per annum

Time = 3 years

FORMULA USED:

In case of compound interest:

Amount = P × (1 + R/100)^T

Where,

P → Principal, R → rate of interest and T → Time

CALCULATION:

Applying the formula:

Amount = P × (1 + R/100)T

13310 = P × (1 + 10/100)³

⇒ 13310 = 1331P/1000

⇒ P = Rs. 10000

∴ Principal amount is Rs. 10000.

Given:

Principal = ₹ 27000

Time = 1 year

Rate of interest = 16%

Formula used:

CI = P (1 + r/100)^t - P

Calculation:

R (when compounded half-yearly) = 16%/2 = 8%

CI = 27000 (1 + 8/100)² - 27000

⇒ (27000 × 1.1664) - 27000

⇒ 31492.8 - 27000

⇒ 4492.8

∴ The compound interest if compounded every six months is 4492.8.

Gi​ven:

Amount = 27 P in 3 years

Concept:

In compound interest, the ratio of the amount and the principal is given by:

Calculation:

We know that,

⇒ R/100 = 3 - 1 = 2

⇒ R = 200%

Hence, the annual interest rate is 200%.

Shortcut Trick

A sum becomes 27 times in 3 years

3^x = 27

⇒ 3^x = 3³

⇒ x = 3

Rate = (x - 1) × 100%

⇒ (3 - 1) × 100% = 200%

∴ The annual interest rate is 200%.

Given:

Principal = Rs. 15,000

Amount = Rs. 19,965

Time = 15 months

Condition = on every 5 months

Concept used:

Condition = on every 5 months

New rate = Rate × 5/12

New time = Time × 12/5

Calculations:

Let the new rate be R%

According to the question,

New time = Time × 12/5

⇒ 15 × 12/5 = 36 months = 3 years

Simplifying the values by dividing it by 15 to its lowest possible values, we get Principal = 1000 and Amount = 1331

Now, new time period is 3 years, hence taking the cube roots of Principal and Amount,

⇒ R = 10%

New rate = Rate × 5/12

⇒ 10 = Rate × 5/12

⇒ Rate = (10 × 12)/5

⇒ Rate = 24%

∴ Rate is 24% per annum.

Alternate MethodGiven:

Principal = Rs. 15,000

Amount = Rs. 19,965

Time = 15 months

Condition = on every 5 months

Concept used:

Condition = on every 5 months

New rate = Rate × 5/12

New time = Time × 12/5

Formulae used:

(1) Effective rate for 3 years = 3R + 3R²/100 + R³/10000

(2) A = P(1 + R/100)^T

Where, A → Amount

P → Principal

R → Rate of interest

T → Time

Calculations:

According to the question,

Let the new rate be R%

New time = Time × 12/5

⇒ 15 × 12/5 = 36 months = 3 years

Amount = P(1 + R/100)^T

⇒ 19,965 = 15,000(1 + R/100)³

⇒ 19,965/15,000 = (1 + R/100)³

⇒ 1331/1000 = (1 + R/100)³

⇒ (11/10)³ = (1 + R/100)³

⇒ 11/10 = 1 + R/100

⇒ (11/10) – 1 = R/100

⇒ 1/10 = R/100

⇒ R = 10%

New rate = Rate × 5/12

⇒ 10 = Rate × 5/12

⇒ Rate = (10 × 12)/5

⇒ Rate = 24%

∴ Rate is 24% per annum

Additional InformationCompound Interest means interest earned on interest. Simple interest always occurs on only principal but compound interest also occurs on simple interest. So, if time period is 2 years, compound interest will also apply on simple interest of first year.

Given:

Principal = Rs.12000 

Time = 5 years 

Formulas used:

Amount = Principal × (1 + r/100)ⁿ

Calculation:

Amount = Principal × (1 + r/100)⁵

⇒ 24000 = 12000 × (1 + r/100)5

⇒ 24000/12000 = (1 + r/100)5

⇒ 2 = (1 + r/100)5          (1) 

⇒ At the end of 15 years, 

⇒ Amount = 12000 × (1 + r/100)¹⁵

⇒ Amount = 12000 × [(1 + r/100)⁵ ]³       (From 1) 

⇒12000 × 2³

⇒12000 × 8 

⇒ 96000 

∴ The amount at the end of 15 years will be Rs.96000

Shortcut Trick 

∴ The amount at the end of 15 years will be 8 times of 12000 = Rs.96000

Given: 

Hari invested Rs.100 for three years at a simple interest rate of 11.03%.

Tipu invested a sum for three years at 10%.

Concept used:

Simple Interest, SI = (P × R × T)/100

Compound interest, CI = P(1 + R/100)ⁿ - P

Calculation:

Let the principal amount that Tipu invested be Rs. P.

After three years,

Hari gets simple interest on the sum he invested,

⇒ (100 × 11.03 × 3)/100

⇒ Rs. 33.09

Tipu gets compound interest on the sum he invested,

⇒ [P × (1 + 10/100)³] - P

⇒ P × 0.331

According to the question,

P × 0.331 = 33.09

⇒ P = 99.969..

⇒ P ≈ 100

∴ Tipu should invest Rs. 100 to get the same amount after three years but at 10% compound interest.

Shortcut Trick S.I = (P × R × t)/100

⇒  = 33.09

Amount = Principal + S.I

⇒ 100 + 33.09 = 133.09

Successive % = a + b + c +  + 

Here, a = b = c = 10%

Successive % = 10 + 10 + 10 + (300/100) + 1000/10000

Successive % =  33.1%

Compound interest 10% in 3 years

⇒  × 100 = Rs.100

Given:

Principal = Rs.13000 

Rate of interest = 15%

Concept used:

Rate of interest for 12 months = 15%

Rate of interest for 8 months = 15 × (8/12) = 10%

And 2 years = 24 months

Total 8-monthly time = 24/8 = 3

Formula:

Let P = Principal, R = rate of interest and n = time period

Compound interest = P(1 + R/100)ⁿ  - P

Calculation:

∴ Compound interest = 13000(1 + 10/100)³  - 13000

⇒ 13000 × (1331/1000)

⇒ 17303 - 13000

= Rs.4303

Given:

The Sum becomes Rs. 7800 in 3 years and Rs. 11232 in 5 years

Formula used:

At compound interest, the final amount = 

Where, P = The sum of the amount

r = Rate of interest

n = Time (years)

Calculation:

Here, Rs. 7800 becomes Rs. 11232 at compound interest in two years.

Let, the rate of interest = R

So, 11232 = 

⇒ [(100 + R)/100]² = 11232/7800

⇒ [(100 + R)/100]2 = 144/100

⇒ [(100 + R)/100]2 = (12/10)²

⇒ [(100 + R)/100] = (12/10)

⇒ 100 + R = 1200/10 = 120

⇒ R = 120 - 100 = 20

∴ The rate per cent is 20%

Given:

Lend amount = Rupees 72,000

Rate = 12% per annum

Time = 3 years

Compounded annually

Concept used:

CI = Total amount - Principal

P(1 + R/100)^N - P

Where, P = Principal, R = Rate of interest, N = Time (in years)

Calculation:

Amount at the end of 1st year

⇒ 72000 × (1 + 12/100)

⇒ 72000 × (112/100)

⇒ Rs. 80640 

Amount at the end of 2nd year

⇒ 80640 × (1 + 12/100) 

⇒ 80640 × (112/100) 

⇒ 90316.8 ≈ Rs. 90317

Interest at the end of 3rd year

⇒ 90317 × (1 + 12/100) - 90317

⇒ 90317 × (112/100) - 90317

⇒ 101155 - 90317

⇒ Rs. 10838

∴ The interest for the 3rd year is Rs. 10838.

Shortcut Trick 

Given:

A sum of money at compound interest amounts to Rs. 5,290 in 2 years and to Rs. 6,083.50 in 3 years.

Formula used:

Amount(A) = Principal(P)(1 + R/100)^T

R = rate %, T = Time

Calculation:

According to the question,

A sum of money at compound interest amounts to Rs. 5,290 in 2 years 

⇒ 5290 = P(1 + R/100)²      ----(1)

A sum of money at compound interest amounts to Rs. 6,083.50 in 3 years

⇒ 6083.5 = P(1 + R/100)³      ----(2)

Divide equation 2 by equation 1

⇒ 6083.5/5290 = P(1 + R/100)³/P(1 + R/100)²

⇒ 6083.5/5290 = 1 + R/100

⇒ (6083.5/5290) – 1 = R/100

⇒ 793.5/5290 = R/100

⇒ 15%

∴ The rate of interest per annum is 15%.

Shortcut Trick

In this type of question, always = {(third year amount – second year amount)/second year amount}×  100

⇒ {(6083.5 – 5290)/5290}× 100

⇒ 0.15 × 100

⇒ 15%

∴ The rate of interest per annum is 15%.

Given:

Certain sum amounts to Rs. 1758 in two years and to Rs. 2,021.70 in 3 years at compound interest when compounded annually.

Concept used:

When compounded annually, the amount received at the end of the period is

Amount = P[1 + r/100]t

Where, P = Principal, r = Rate of interest p.a., t = Time period

Calculation:

Let the rate be R%

P(1 + R/100)2 = 1758  ....(i)

P(1 +R/100)3 = 2021.7 ....(ii)

Dividing equation (ii) by (i)

⇒ 1 + R/100 = 2021.7/1758

⇒ R/100 = (2021.7 – 1758)/1758

⇒ R = (263.7 × 100)/1758 = 15%

∴ The rate of interest p.a. is 15%.

Shortcut TrickDifference between the amount of 2 yr and 3 yr = 2021.7 - 1758 = 263.7

Now, this sum of Rs. 263.70 is earned as interest on Rs. 1758 (2 years' SI) taken as principal.

Therefore, the reqd rate % = (263.70/1758) × 100 = 15%.

Given:

Principal = Rs. 60,000

Rate = 9%

Compound Interest = Rs. 11,286

Amount = Principal + Compound Interest

Formula used:

Amount = P(1 + Rate/100)^Time

Amount = Principal + Compound Interest

Calculation:

Amount = 60,000 + 11,286 = 71,286

Amount = P(1 + Rate/100)Time

⇒ 71,286 = 60,000(1 + 9/100)^Time

 ⇒ 71,286 = 60,000[(100 + 9)/100]^Time

⇒ 71,286/60,000 = (109/100)^Time

⇒ (11,881/10,000) = (109/100)^Time

⇒ (109/100)2 = (109/100)Time

⇒ Time = 2

∴ The time period is 2 years.