Question

Tometeo wants to have $50,000 saved 15 years from now. How much must he deposit every month into an account that pays 2.8% interest, compounded monthly?

Answer 1

• $223.84 at the end of the month, or
• $223.31 at the beginning of the month

Explanation:

The annuity formula is used for this.

A = P((1+r/12)^(12t) -1)/(r/12)

gives the balance A resulting from payments P being compounded monthly at annual rate r. (Payments are made at the end of the month.)

50,000 = P((1 +.028/12)^(12·15) -1)/(0.028/12) ≈ 223.378772P

P ≈ 50,000/223.378772 ≈ 223.84

To achieve the desired balance, Tometeo must deposit $223.84 at the end of every month.

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If Tometeo makes his deposits at the beginning of the month, then the amount is less by the interest earned for the month:

$223.84/(1 +.028/12) ≈ $223.31 . . . . beginning of the month deposit amount