Paige has decided that she wants to build enough retirement wealth that, if invested at 5 percent per year, will provide her with $2,500 monthly income for 20 years. To date, she has saved nothing, but she still has 40 years until she retires. How much money does she need to contribute per month to reach her goal?
A) $180.02
B) $248.24
C) $460.81
D) $921.61

Question

Quizplus · Accepted Answer

To solve this, we first need to calculate the present value (PV) of the retirement wealth needed to provide Paige with $2,500 monthly for 20 years at a 5% annual interest rate, converted to a monthly rate (5%/12 months = 0.4167%). Using the present value of an annuity formula, PV = Pmt * [(1 - (1 + r)^-n) / r], where Pmt is the monthly payment ($2,500), r is the monthly interest rate (0.4167%), and n is the total number of payments (20 years * 12 months = 240). This calculation gives us the lump sum Paige needs at the start of her retirement.Next, we calculate how much Paige needs to save monthly for the next 40 years (40 years * 12 months = 480 months) to reach this lump sum, using the future value of a series formula in reverse. We use the same interest rate (0.4167% monthly) to find the monthly contribution.The correct answer involves calculating the present value of the retirement goal and then determining the monthly contribution needed to reach this goal over 40 years at a 5% annual interest rate. The calculations show that Paige needs to contribute $248.24 per month to reach her goal, making option B the correct choice.

Paige Has Decided That She Wants to Build Enough Retirement