Question

At what rate of annual simple interest, sum will amount to five times in 40 years?
(a) 5%
(b) 25%
(c) 50%
(d) 10%

Answer 1

Hint: To solve this problem, we should know the basics of simple interest. The formula to be used in this problem is –
Simple Interest (I) = $\dfrac{\operatorname{P}Rt}{100}$
Total amount (A) = P + $\dfrac{\operatorname{P}Rt}{100}$
Here, P is the principal amount (sum in this case), R is the simple interest rate in percent, t is the time in years for which the money is invested. We will then proceed by using the information in the question that the total amount would be 5 times the principal amount (A = 5P) along with time (t) as 40 years (given in the question) to get the required value of simple interest rate (R).

Complete step-by-step answer:
Before we begin to solve the problem, we try to understand the basics of simple annual interest rate. Simple interest is a quick and easy method of calculating the interest charge on a loan/sum of amount invested. For example, if we have taken a loan of Rs 1000 with annual interest rate of 10% and for 2 years, the simple interest would be $\dfrac{\operatorname{P}Rt}{100}$. Thus, it would be $\dfrac{(1000)(10)(2)}{100}$ = Rs 200. Now, coming back to the problem in hand, we have to find the rate of annual simple interest for which the sum will amount to five times its original amount in 40 years (thus total amount = 5P). Thus, we have,
A (total amount) = P + $\dfrac{\operatorname{P}Rt}{100}$ (where, P’ is the new sum after 5 years, which is 5 times the original amount)
5P = P + $\dfrac{\operatorname{P}Rt}{100}$
4P = $\dfrac{\operatorname{P}Rt}{100}$

4 = $\dfrac{Rt}{100}$
4 = $\dfrac{R(40)}{100}$
R = 10%
Hence, the correct option is (d) 10%.

Note: We should be careful about the difference between the total amount and simple interest while solving these problems. Simple interest is the additional amount that would be added to the principal amount (which is invested/borrowed) after a certain time of investing. The total amount however is the simple interest plus the original principal amount.