Solve the problem.
-A 49-year-old man deposits a total of $2000 per year in an IRA until age 65. How much money will be in the account if the interest rate is 8% compounded semiannually with payments of $1000 made at the end of each semiannual period?

Question

Solve the problem. 
-A 49-year-old man deposits a total of $2000 per year in an IRA until age 65. How much money will be in the account if the interest rate is 8% compounded semiannually with payments of $1000 made at the end of each semiannual period?

Quizplus · Accepted Answer

The correct answer is A because the future value of the annuity is calculated as follows:FV = P * [(1 + r/n)^(n*t) - 1] / (r/n)where:P = $1000 (semiannual payment)r = 8% (annual interest rate)n = 2 (number of compounding periods per year)t = 16 (number of years)FV = $1000 * [(1 + 0.08/2)^(2*16) - 1] / (0.08/2)FV = $1000 * [(1.04)^32 - 1] / 0.04FV = $1000 * [2.191123 - 1] / 0.04FV = $1000 * 1.191123 / 0.04FV = $29,778.08Since the man deposits $2000 per year, the total amount in the account will be $29,778.08 * 2 = $59,556.16. However, the question asks for the amount in the account, which includes the initial deposits. Therefore, the total amount in the account is $59,556.16 + $2000 = $61,556.16.

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