You currently have $150,000 in an IRA designated for retirement. If you save an additional $100 at the end of every month and expect to earn an annual return of 12 percent, how much do you expect to have in the IRA in 10 years?
A) $467,632
B) $518,062
C) $732,546
D) $949,328
E) $1,215,234

Question

Quizplus · Accepted Answer

To solve this, we use the future value formula for an annuity to calculate the future value of the monthly contributions and add it to the future value of the lump sum investment. The future value of the lump sum (the initial $150,000) can be calculated using the formula FV = PV * (1 + r)^n, where PV is the present value, r is the annual interest rate (expressed as a decimal), and n is the number of periods. For the monthly contributions, we use the future value of an annuity formula: FV = P * [((1 + r)^n - 1) / r], where P is the payment amount, r is the monthly interest rate, and n is the total number of payments.Given:- Initial investment (PV) = $150,000- Monthly contribution = $100- Annual interest rate = 12% or 0.12 (monthly interest rate = 0.12/12 = 0.01)- Number of years = 10 (number of months n = 10*12 = 120)First, calculate the future value of the initial investment:FV (lump sum) = $150,000 * (1 + 0.12)^10 ≈ $442,593Then, calculate the future value of the monthly contributions:FV (annuity) = $100 * [((1 + 0.01)^120 - 1) / 0.01] ≈ $75,469Adding both future values gives the total amount in the IRA in 10 years:Total FV ≈ $442,593 + $75,469 ≈ $518,062Therefore, the correct answer is B) $518,062.

You Currently Have $150,000 in an IRA Designated for Retirement