Question

Justin is saving for a wedding. He wishes to have $30,000 saved up in 4 years. How much should he deposit now if the rate is 5% compounded monthly?

a) $22,987.63
b) $27,336.87
c) $25,000.00
d) $30,000.00

Answer 1

Justin should deposit $22,987.63 now if he wants to have $30,000 in 4 years with a 5% interest rate compounded monthly.

Step-by-step explanation:

To determine how much Justin should deposit now to have $30,000 in 4 years with a 5% interest rate compounded monthly, we can use the formula for compound interest: P = A / (1 + r/n)nt, where P is the principal (initial amount deposited), A is the future value desired, r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the number of years the money is invested.

Given that A = $30,000, r = 0.05 (5% annual interest rate), n = 12 (interest is compounded monthly), and t = 4 years, we can find P using the formula:

Convert the annual rate to a monthly rate by dividing by 12: r/n = 0.05/12

Calculate the total number of periods by multiplying the number of years by 12: nt = 4*12

Insert these values into the formula to solve for P.

Carrying out the calculations, Justin needs to deposit $22,987.63 now to have $30,000 in 4 years at a 5% interest rate compounded monthly, which corresponds to option a) $22,987.63.