How much would your parents have to deposit each month into an account that grows at a rate of 8% per year compounded semi-annually if they want to have $84,000 at the end of year 3 to cover part of your college expenses?

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Business

Obie

11 November, 18:56

How much would your parents have to deposit each month into an account that grows at a rate of 8% per year compounded semi-annually if they want to have $84,000 at the end of year 3 to cover part of your college expenses?

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Hanson · Answer 1

Monthly Payment = $2,067.25924

Explanation:

To find the value of the monthly deposit, e use the Future Value of Annuity Payments formula as follows

Future Value of Annuity = p x (1+r) ∧n-1) / r

step 1: We determine the effective rate as follows

= (1 + (0.08/2) ∧2) - 1

= 1.08160 - 1

= 0.0816 or 8.16%

Step 2: We determine the monthly rate of r to allow for compounding of interest

= 8.16% / 12 months = 0.68% = r

n = Number of months = 3 years x 12 months = 36 months

Future value of the annuity = $84,000

Therefore find P which is the monthly payment as follows

= $84,000 = P x (1 + 0.0068) ∧ 36-1) 0.0068

= $84,000 = P x (0.276307871/0.0068

84,000 = p x 40.63351044

P = $84,000 / 40.63351044

P = $2,067.25924