Question

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?

Answer 1

MP = $256.30

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

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.

Answer 2

$2,221.6 monthly

Explanation:

A = P(1 + r)^n

A is the total amount I intend to save = $15,000

r is the yearly interest rate = 3.6% = 0.036

n is the duration to achieve my goal = 4 and 1/2 years = 54 months

15,000 = P(1 + 0.036)^54

15,000 = P(1.036)^54

P = 15,000/6.752 = 2,221.6

I need to put $2,221.6 into the savings account monthly