Question

Raj deposits 50 into a fund at the end of each month for 5 years. The fund pays interest at an annual effective rate of i. The total amount of interest earned during the last month of year 5 is 13. Calculate the accumulated amount in Raj's account at the end of year 5

A) 3325

B) 3350

C) 3375

D) 3400

E) 3425

Answer 1

This can be solved by trial and error

let us construct a schedule of investment value using 5% interest rate as below :

First deposit is made at the end of 1st month, so interest is zero in 1st month

In the second month onward until 60th month,

interest = beginning value * interest rate / 12   (as the interest is calculated monthly)

ending value = beginning value + interest + deposit

With 5% interest rate, the ending value and interest paid in last month of year 5 are as below :

In the question, the interest paid in last month of year 5 is 13. So we try again with a lower interest rate of 4.5% :

Interest paid in last month of year 5 is 12.36. We try again with 4.71% interest :

With 4.71% interest rate ,we can see that the interest paid in last month of year 5 exactly equals 13.00

The ending value of this investment is 3,375.26

The answer is C