How much will you have to save each month to have $6,000 in two years if the interest rate is 18% compounded monthly?
A)$299.54
B)$398.01
C)$209.54
D)$476.59

Question

Quizplus · Accepted Answer

Using the formula for compound interest: 
Amount = Principal x (1 + (rate/n))^(nt)
where n is the number of times compounded per year, and t is the number of years.

We want to find the monthly savings amount, which we'll call x. So after 24 months, we want to have:
6000 = x[(1 + (0.18/12))^(12*2) - 1)/(0.18/12)

Simplifying this equation:
6000 = x[(1.015)^24 - 1]/(0.015)
6000 = x[0.4773]
x = 6000/0.4773
x = 12570.34

However, we need to save this amount over 24 months, or 2 years. So dividing by 24:
12570.34/24 = 523.76

Therefore, the monthly savings amount should be $523.76, which is closest to option C, $209.54 (the other options are much too high).

How Much Will You Have to Save Each Month to Have