Suppose that you begin saving up to buy a car by depositing a certain amount at the end of each month in a savings account which pays 3.6% annual interest compounded monthly. If your goal is to have $15,000 in the account four and a half years from now, how much do you need to put into the savings account each month?

MP = $256.30

Therefore, you need to put $256.30 per month into the savings account at the end of each month.

Step-by-step explanation:

The future value of an investment paid at the end of each month with interest compounded monthly can be written as;

A = MP * {[ (1 + r/n) ⁿᵗ - 1] / (r/n) }

MP = A : {[ (1 + r/n) ⁿᵗ - 1] / (r/n) } ... 1

Where;

A = future value of investment = $15,000

MP = monthly payment at the end of the month

r = interest rate = 3.6% = 0.036

t = time = 4.5 years

n = number of times the interest is compounded = 12

Substituting the values into equation 1

MP = 15000 : {[ (1 + 0.036/12) ^ (12*4.5) - 1] / (0.036/12) }

MP = 15000 : 58.52503734772

MP = $256.30

Therefore, you need to put $256.30 per month into the savings account at the end of each month.