Question

Leo did not start saving for his retirement when he started working. Instead, he waited until age forty. Now he only has 26 years to save for retirement. Assume that he puts the $300 per month into his IRA. At a 9.8% average annual return how much would have Leon have for contributions made at the beginning of the month?

a. $463,588.93

b. $459,681.63

c. $427,956.75

d. $431,451.73

Answer 1

Given,

Monthly deposit (M) = $300

No. of years = 26 years

Annual return = 9.8% or 0.098

Solution :-

No. of months (n) = 26 years x 12 months = 312 months

Monthly return (r) = 0.098/12 = 0.0081666667

Future value = M/r x [(1 + r)ⁿ - 1] x (1 + r)

= $300/0.0081666667 x [(1 + 0.0081666667)³¹² - 1] x (1 + 0.0081666667)

= $300/0.0081666667 x [(1.0081666667)³¹² - 1] x (1.0081666667)

= $300/0.0081666667 x [12.64993375 - 1] x (1.0081666667)

= $300/0.0081666667 x 11.64993375 x 1.0081666667 = $431451.73

Thus, Leon would have $431451.73 for contributions made at the beginning of the month.