Question

A woman deposits $12,000 at the end of each year for 12 years in an investment account with a guaranteed interest

rate of 5% compounded annually.
(a) Find the value in the account at the end of the 12 years.
(b) Her sister works for an investment firm that pays 4% compounded annually. If the woman deposits money with this
firm instead of the one in part (a), how much will she have in her account at the end of 12 years?
(c) How much would she lose or gain over 12 years by investing in her sister's firm?

Answer 1

(a) $191,005.52

(b) $180,309.67

(c) lose $10,695.85

Explanation:

You want the future values of an ordinary annuity of $12,000 over 12 years at interest rates of 5% and 4%. You also want the difference between the values.

(a) 5%

The future value of an ordinary annuity with n annual deposits of P, at interest rate r compounded annually is given by ...

FV = P((1+r)^n -1)/r

The value of $12,000 deposited for 12 years at 5% is ...

FV = $12,000((1.05^12 -1)/0.05 = $191,005.52

At the end of 12 years, she will have $192,005.52 in her account.

(b) 4%

The value of $12,000 deposited for 12 years at 4% is ...

FV = $12,000((1.04^12 -1)/0.04 = $180,309.67

At the end of 12 years, she will have $180,309.67 in her account.

(c) difference

The amount at 5% is greater, so by investing in her sister's firm, the woman would lose ...

$192,005.52 -180,309.67 = $10,695.85 . . . . amount lost