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 :

D3 A -83*5%/12 Beginning 1 Month Value Deposit Interest Ending Value 50.00 100.21 150.63 201.25 252.09 303.14 354.41 405.88 457.57 1 2 3 100.21 4 150.63 50.00 50.00 50.00 50.00 5 201.2550.00 50.00 7 303.1450.00 50.00 50.00 0.00 0.00 0.21 0.42 0.63 0.84 1.05 1.26 1.48 1.69 50.00 4 6 252.09 354.41 10 405.88

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 :

D61 fel-B61*5%/12 Beginning 1 Month Value 57 58 59 Deposit Interest Ending Value 3,146.28 56 3,083.4450.00 12.85 57 3,146.2850.00 13.11 58 3,209.3950.00 13.373,272.77 9 3,272.77 50.00 13.64 60 3,336.40 13.643,336.40 1.x) 61

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% :

D4 fel -84*4.5%/12 Beginning 1 2 Month Value Deposit Interest Ending Value .00 50.00 0.00 1 250.00 50.00 3 100.1950.00 0.19 01. 50.00 100.19 150.56 4

D61 fel -861*4.5%/12 Beginning 1 Month Value 57 58 59 60 61 Deposit Interest Ending Value 3,109.25 56 3,047.82 50.00 11.43 573,109.2550.00 11.66 7 3,109.25 583,170.9150.00 11.89 59 3,232.80 50.00 12.12 60 3,294.92 3,232.80 3,294.92 3,357.28

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

D3 fy -83*4.71%/12 Beginning 1 Month Value 1 2 3 100.20 50.00 4 150.59 5 201.1850.00 Deposit Interest Ending Value 50.00 100.20 150.59 201.18 251.97 0.00 50.00 0.00 0.20 0.39 0.59 0.79 50.00 50.00 4 50.00

D61 fl -861*4.71%/12 Beginning 1 Month Value 56 57 58 59 55 3,000.9350.00 56 3,062.71 50.00 12.02 57 583,187.0050.00 12.51 59 3,249.5 Deposit Interest Ending Value 11.783,062.71 3,124.73 3,124.73 50.00 12.26 3,187.00 150.00 12.75 3,312.26 3,375.26 61 60 3,312.26

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