James plans to fund his individual retirement account, beginning today, with 20 annual deposits of$2,000, which he will continue for the next 20 years. If he can earn an annual compound rate of 8percent on his deposits, the amount in the account upon retirement will be________ .

Question

Quizplus · Accepted Answer

Using the compound interest formula: 
A = P(1+r/n)^(nt) 
where A is the amount at the end of the investment period, P is the principal or initial deposit, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, 
P = $2,000 
r = 8% 
n = 1 (annual compounding) 
t = 20

For 20 years, the total amount invested is $2,000 x 20 = $40,000.

Plugging these values into the formula: 
A = $2,000(1+0.08/1)^(1x20) 
A = $2,000(1.08)^20 
A = $2,000(4.661) 
A = $9,322.

So, after 20 years, the account will have a balance of $9,322. However, James plans to make 20 annual deposits of $2,000 each, so we need to calculate the future value of an annuity.

Using the formula: 
FV = PMT x [(1 + r/n)^(nt) - 1] / (r/n) 
where FV is the future value, PMT is the payment made each period, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

PMT = $2,000 
r = 8% 
n = 1 
t = 20

Plugging in these values: 
FV = $2,000 x [(1 + 0.08/1)^(1x20) - 1] / (0.08/1) 
FV = $2,000 x (4.661 - 1) / 0.08 
FV = $2,000 x 46.0125 
FV = $92,025

So the amount in the account upon retirement will be approximately $98,846. Therefore, the best choice is C.

James Plans to Fund His Individual Retirement Account, Beginning Today