Question

Jackson wants to have $18,000 available to buy a motorcycle in three years. How much should Jackson save each month if he earns 5% interest, compounded monthly?

a. $502.23
b. $498.74
c. $507.89
d. $490.65

Answer 1

To find out how much Jackson needs to save monthly for $18,000 with a 5% interest rate compounded monthly over 3 years, the correct monthly savings is approximately $502.23.

Step-by-step explanation:

Jackson wants to save a total of $18,000 in three years to buy a motorcycle, with an interest rate of 5% compounded monthly. To find out how much he should save each month, we can use the formula for the future value of an annuity:

Future Value (FV) = Pmt × ((1 + r)^n - 1) / r

Where:

• Pmt is the monthly payment
• r is the monthly interest rate (annual rate divided by 12)
• n is the total number of payments (months)

First, we convert the annual interest rate to a monthly interest rate: 5% annually is about 0.05/12 per month. Then, since there are 3 years or 36 months within which to save, we can plug the values into our formula:

$18,000 = Pmt × ((1 + 0.05/12)^36 - 1) / (0.05/12)

Now, we solve for Pmt (the monthly payment):

Pmt = $18,000 / (((1 + 0.05/12)^36 - 1) / (0.05/12))

After calculating, we find that the monthly payment Jackson should make is approximately $502.23, which corresponds to option (a).