Jim will retire in 30 years.He will invest $100 each month for 15 years and then let the accumulated value continue to grow for the next 15 years.How much will be available at retirement? Assume 9%,
Compounded monthly.Round to the nearest dollar.
A)$130,692
B)$145,234
C)$139,399
D)$145,207
E)$138,014

Question

Quizplus · Accepted Answer

To solve this problem we need to use the formula for future value of an annuity:

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

where FV is the future value, PMT is the monthly investment amount, r is the interest rate per month (9%/12), and n is the total number of months (15 years x 12 months/year = 180 months).

Using this formula, we can calculate the future value of Jim's investments after 15 years:

FV = 100 x (((1 + 0.0075)^180 - 1) / 0.0075) = $30,687

This means that after 15 years, Jim will have $30,687 saved up.

Next, we need to calculate the future value of this amount after another 15 years of compounding at 9% per year. To do this, we can use the formula for future value of a lump sum:

FV = PV x (1 + r)^n

where PV is the present value (in this case, $30,687), r is the interest rate per year (9%), and n is the total number of years (15).

Using this formula, we get:

FV = 30,687 x (1 + 0.09)^15 = $145,234

So the total amount available at retirement will be $145,234.

Therefore, the best choice is B.

Jim Will Retire in 30 Years