Question

Stan has made a $125.30 monthly deposit into an account that pays 1.5% interest, compounded monthly, for 35 years. he would now like to draw a monthly salary from the account. determine the amount that stan can withdraw each month for 20 years, if he plans on not having anything in the account at the end of the 20 year period and no future deposits are made to the account. a. $69,242.49 b. $69,159.05 c. $333.29 d. $333.71

Answer 1

The annuity of the monthly deposit into an account that pays 1.5% interest, compounded monthly, for 35 years is $333.71

What is annuity?

An annuity is a series of payments made at equal period of time.

future value = annuity x [(1 + i)ⁿ - 1] / i

annuity = $125.30

i = 1.5% / 12 = 0.00125

n = 35 years x 12 months = 420

future value = $125.30 x [(1 + 0.00125)⁴²⁰ - 1] / 0.00125

future value = $69,156.049 ≈ $69,156.05

annuity = [i x (present value)] / [1 - (1 + i)⁻ⁿ]

i = 1.5% / 12 = 0.00125

n = 20 years x 12 months = 240

present value = $69,156.05

annuity = (0.00125 x $69,156.05) / [1 - (1 + 0.00125)⁻²⁴⁰]

annuity = $86.45 / 0.25904

= $333.71

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