Question

How many months will it take to save $5000 by making deposits of $80 at the end of every month into an account earning interest at 4.2% compounded monthly?

Select one:

a. 62

b. 71

c. 57

d. 63

Answer 1

Option (c) is correct

Here, the deposits will be same every month, so it is an annuity. The future value of annuity is $5000. Here we will use the future value of annuity formula as per below:

FVA = P * ((1 + r)ⁿ - 1 / r)

where, FVA is future value of annuity = $5000, P is the periodical amount = $80, r is the rate of interest = 4.2% compounded monthly, so monthly rate is 4.2% / 12 = 0.35% and n is the time period

Now, putting these values in the above formula, we get,

$5000 = $80 * ((1 + 0.35%)ⁿ - 1 / 0.35%)

$5000 / $80 = ((1 + 0.0035)ⁿ - 1 / 0.0035)

62.5 = ((1.0035)ⁿ - 1 / 0.0035)

62.5 * 0.0035 = ((1.0035)ⁿ- 1))

0.21875 = ((1.0035)ⁿ - 1))

0.21875 + 1 =  (1.0035)ⁿ

1.21875 = (1.0035)ⁿ

(1.0035)⁵⁷ = (1.0035)

n = 57

So, it will take 57 months approx.