Compound Interest – Formulas, Aptitude Questions and Answers with Explanation, Tips and Tricks (Solved Examples on Interest Payable, Amount, Simple Interest)

Formulas and Quick Tricks for Compound Interest

1. Generally, Compound Interest, CI_yearly = P [1 + R/100]ⁿ, where P is the prinicipal sum of money, R is the interest rate and n is the time period in years.
2. Amount, A = P [ 100+R / 100 ]ⁿ, if interest is payable annually
3. Amount, A = P [ 100+R' / 100 ]^n', R’= R/2, n’ = 2n; if interest is payable half-yearly
4. Amount, A = P [ 100+R'' / 100 ]^n'', R’’ = R/4, n’’ = 4n; if interest is payable quarterly
5. When Rates are different for different years, say, R₁, R₂, R₃ for 1st, 2nd and 3rd years respectively, then Amount = P(100+R₁ / 100) (100+R₂ / 100) (100+R₃ / 100)
6. In general, interest is considered to be Simple unless otherwise stated.

Questions and Solved Examples on Compound Interest

Q.1: The principle that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?
A. Rs. 3096
B. Rs. 4076
C. Rs. 4085
D. Rs. 4096
Answer: D. Rs. 4096
Explanation: According to the formula,
Principle = [4913 / (1 + 25/ (4 * 100))3]
=> 4913 * 16/17 * 16/17 * 16/17 = Rs. 4096

Q.2: Find the Compound Interest on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?
A. Rs. 1,185
B. Rs. 1,261
C. Rs. 1,346
D. Rs. 1,440
Answer: B. Rs. 1,261
Explanation: A = 8000(21/20)^3 = 9261
Now, 9261 – 8000 = Rs. 1,261


Q.3: The difference between simple interest and C.I. at the same rate for Rs.5000 for 2 years in Rs.72. The rate of interest is?
A. 6%
B. 8%
C. 10%
D. 12%
Answer: D. 12%
Explanation: 5000 = 72(100/R)^2
5 R^2 = 720 => R = 12

Q.4: The difference between compound and simple interest on a certain sum of money for 3 years at 6 2/3% p.a is Rs.184. Find the sum?
A. Rs.12,000
B. Rs.13,500
C. Rs.14,200
D. Rs.17,400
Answer: B. Rs.13,500
Explanation: P = (184*10^6) / [6 2/3 * 6 2/3 *(300*6 2/3)]
P = 13500

Q.5: A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.482 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum.
A. Rs.1,000
B. Rs.1,250
C. Rs.2,000
D. Rs.4,000
Answer: C. Rs.2,000
Explanation: P(11/10)^4 – P(6/5)^2 = 482
P = 2000

Q.6: The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal?
A. Rs.3,000
B. Rs.3,300
C. Rs.3,600
D. Rs.3,900
Answer: C. Rs.3,600
Explanation: P = 144(100/5)^2 => P = 3600

Q.7: Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?
A. Rs.9,021
B. Rs.9,162
C. Rs.9,261
D. Rs.9,621
Answer: C. Rs.9,261
Explanation: A = 8000(21/20)^3 = 9261

Q.8: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000?
A. Rs.61,000
B. Rs.65,000
C. Rs.71,000
D. Rs.81,000
Answer: D. Rs.81,000
Explanation: 64000* 9/8 * 9/8 = 81000


Q.9: Indu gave Bindu Rs.1250 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
A. Rs.10
B. Rs.5
C. Rs.3
D. Rs.2
Answer: D. Rs.2
Explanation: 1250 = D(100/4)^2
D = 2

Q.10: How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
A. Rs.424
B. Rs.482
C. Rs.512
D. Rs.842
Answer: B. Rs.482
Explanation: 20000(11/10)^4 – 20000(6/5)^2 = 482