Simple Interest Solved example Problems

1. At what rate percent per annum will a sum of money double in 16 years?
Explanation:
 Let principal = P. Then, S.I. = P and T = 16 years
=> Rate = [100 * P / P * 16]% 
        = 6 1/4% p.a

2. The simple interest on a sum of money is 4/9 of the principal. Find the rate percent and time, if both are numerically equal.
Explanation:
Let sum = Rs. x Then, S.I. = Rs. 4x/9
Let rate = R% and time = R years.
Then, [x * R * R / 100] = 4x / 9 or R² = 400/9 or R = 20/3 = 6 2/3
=> Rate = 6 2/3 % and Time = 6 2/3 yrs 
                           = 6 yrs 8 months.

3. A sum was put at simple interest at a certain rate for 3 years. Had it been put at 2% higher rate, it would have fetched Rs. 360 more. Find the sum.
Explanation:
Let sum = P and original rate = R. Then,
[P * (R+2) * 3 / 100] - [P * R * 3 / 100] = 360
=> 7x/20 - 3x/10 = 40 
=> x = (40 * 20) = 800.
Hence, the sum is Rs. 800.

4. Find the simple interest on Rs. 68,000 at 16 2/3 % per annum for 9 months.
 Explanation:
Let sum = P and original rate = R. Then,
[P * (R+2) * 3 / 100] - [P * R * 3 / 100] = 360
=> 7x/20 - 3x/10 = 40 
=> x = (40 * 20) = 800.
Hence, the sum is Rs. 800.

5. Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
Explanation:
Let rate = R% and time = R years. Then
(1200 x R x R / 100) ‹=› 432
‹=›12R2 = 432
‹=›R2 = 36
‹=› R = 6