Question

A woman deposits $14,000 at the end of each year for 10 years in an investment account with a guaranteed interest rate of 4% compounded annually.

 (a) Find the value in the account at the end of the 10 years.

 (b) Her sister works for an investment firm that pays 3% 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 10 years?

 (c) How much would she lose or gain over 10 years by investing in her sister's firm? The value in the account at the end of the 10 years will be $nothing. (Do not round until the final answer. Then round to the nearest cent as needed.). Find the future value for the ordinary annuity with the given payment and interest rate.

Answer 1

To find the accumulated value after 10 years, the formula is;

Amount of investment* ((1+interest)^number of years - 1)/interest rate

In the given case, value in her account after 10 years at 4% rate of interest annual componding = 14000*((1+0.04)^10-1)/0.04 = $168,085.5

If the rate of interest is 3%, the value is = 14000*(1+0.03)^10-1)/0.03 = $160494.3

Net Loss on investing in sister concern = 168085.5 - 160494.3 = $7,591.2