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Get interested in solving these ‘simple’ interest problems

Hyderabad: This article is in continuation to the last article on preparation for the Sub-Inspector of Police recruitment exam. Here are some practice questions and answers along with explanations on the Simple Interest and Compound Interest topic. 1. A sum of money at compound interest amounts to thrice itself in three years. In how many […]

Hyderabad: This article is in continuation to the last article on preparation for the Sub-Inspector of Police recruitment exam. Here are some practice questions and answers along with explanations on the Simple Interest and Compound Interest topic.

1. A sum of money at compound interest amounts to thrice itself in three years. In how many years will it be 9 times itself?
A. 6 B. 9 C. 12 D. 18 Ans: A

Explanation:
Given that 3P = P (1 r/100) 3
(1 r/100)3 = 3P/P = 3 ——— (1)
Let us assume P (1 r/100)n = 9P
(1 r/100)n = 9 = 3^2
Substitute eq (1) here =>; (1 r/100)n = ((1 r/100)3)2 = (1 r/100)6
Therefore, the amount becomes 9 times in 6 years

2. The compound interest on a certain sum of money for two years is Rs 41 and the simple interest is Rs 40. Then the rate per annum is
A. 4% B. 5% C. 6% D. 8% Ans: B

Explanation:
Difference between compound interest and simple interest on certain money for two years is equal to the interest on interest for the first year
Here difference = 41 – 40 = Rs 1
Interest for the first year = 40/2 = Rs 20 (in simple interest, interest is same for ll years)
Rate of interest = 1/20 × 100 = 5%

3. What is the compound interest on Rs 5,000 for 4 years, if the rate of interest is 10% p.a. for the first two years and 20% p.a. for the next 2 years?
A. Rs 3,312 B. Rs 3,712 C. Rs 3,750 D. Rs 3,350 Ans: B

Explanation:
Amount for the 1st 2 years = P (1 R/100)T
= 5000 (1 (10/100))2
= 5000(11/10)2 = 5000 × 121/100 = 6050
Principal for the next 2 years = 6050
Amount for the 2nd 2 years = P (1 R/100)T
= 6050(1 (20/100))2 = 6050 × (6/5)2
6050 × (36/25) = Rs 8712
Interest = Amount – Principal = 8712 – 5000 = Rs 3712

4. What is the compound interest on Rs 4,000 at 10% p.a. for two years and three months?
A. Rs 912 B. Rs 961 C. Rs 990 D. Rs 900 Ans: B

Explanation:
If the interest is compound annually but time is in fraction say 5 3/2 years then Amount
A = P (1 R/100)5 × [1 (3/2R)/100]
Here T = two years 3 months = 2.25
A = 4000(1 (10/100))2 × (1 (1/4 ×10)/100) = 4000 × 11/10 × 11/10 × 41/40 = 4961
Interest = Amount – Principal = 4961 – 4000 = 961

5. Rs 7,500 is invested at 5% compound interest for two years. What is the interest for the second year?
A. Rs 306.25 B. Rs 375.75 C. Rs 393.75 D. Rs 326.25 Ans: C

Explanation:
Interest for the 1st year = 5% of 7500 = 7500 × 5/100 = 375
First year amount equal to second year principal
Amount for the first year = 7500 375 = 7875
Interest for the second year = 5% of 7875 = 7875× 5/100 = 393.75.

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