Edward Johnson decided to open up a Roth IRA. He will invest $1,800 per year for the next 35 years. Deposits to the Roth IRA will be made via a $150 payroll deduction at the end of each month. Assume that Edward will earn 8.75% annual interest compounded monthly over the life of the IRA. How much will he have at the end of 35 years?
A) $125,250
B) $250,321
C) $363,000
D) $414,405

Question

Quizplus · Accepted Answer

To solve this problem, we can use the formula for future value of an annuity with monthly compounding:

FV = PMT x (((1 + r)^n - 1) / r)

where:

PMT = monthly deposit ($150)
r = monthly interest rate (8.75% / 12 = 0.007292)
n = number of months (35 years x 12 months = 420)

First, we can calculate the future value of the monthly deposits:

FV_monthly = 150 x (((1 + 0.007292)^420 - 1) / 0.007292) = $209,166.92

Next, we can calculate the future value of the annual contributions:

FV_annual = 1,800 x (1 + 0.0875)^35 = $221,238.17

Finally, we can add the two future values together to get the total value of the Roth IRA:

FV_total = FV_monthly + FV_annual = $209,166.92 + $221,238.17 = $430,405.09

Therefore, the best choice is (D), $414,405.

Edward Johnson Decided to Open Up a Roth IRA