Question

Francine currently has $25,000 in her 401k account at work, and plans to contribute $300 at the end of each month for the next 10 years. How much will she have in the account in 10 years, if the account averages a 4% annual return? Assume monthly compounding. Asnwer = $ (Round to the nearest cent/penny)

Answer 1

Given,

Current balance = $25000

Monthly contribution = $300

Annual return = 4% or 0.04

Number of years = 10 years

Solution :-

Monthly interest rate (r) = 0.04/12 = 0.00333333333

Number of months (n) = 10 years x 12 = 120

Now,

Future value = [Current balance x (1 + r)ⁿ] + [monthly contribution/r x [(1 + r)ⁿ - 1]

= [$25000 x (1 + 0.00333333333)¹²⁰] + [$300/0.00333333333 x {(1 + 0.00333333333)¹²⁰ - 1}]

= [$25000 x (1.00333333333)¹²⁰] + [$300/0.00333333333 x {(1.00333333333)¹²⁰ - 1}]

= [$25000 x 1.49083268182] + [$300/0.00333333333 x {1.49083268182 - 1}]

= [$37270.8170455] + [$300/0.00333333333 x 0.49083268182]

= $37270.8170455 + $44174.9414079

= $81445.76

She will have $81445.76 in the account in 10 years.