step by step You invested 2000 at the end of each year for 7

step by step

You invested $2,000 at the end of each year for 7 years and your investment was worth $16,788 at the end of the investment period. What was the annual rate of interest earned on this investment if interest was compounded annually? o 490 ? 6% O 20% The answer cannot be computed without additional information

Solution

Solution 1:

Annual installment = $2000

Time period = 7 years

Future value of investment at the end of 7 years = $16788

Let annaul rate of interest = X%

Annual Installment * Cumulative FV factor @X% for 7 periods = Future value of Investment

$2000 *Cumulative FV factor @X% for 7 periods = $16788

Cumulative FV factor @X% for 7 periods = $16788/ $2000

Cumulative FV factor @X% for 7 periods = 8.394

By referring annuity table, this Cumulative FV factor for 7 periods falls at 6%.

therefore X = 6%

Hence second option \"6%\" is correct.

Solution 2:

Annual installment = $10,000

Time period = 10 years

Future value of investment at the end of 7 years = $138,164

Let annaul rate of interest = X%

Annual Installment * Cumulative FV factor @X% for 10 periods = Future value of Investment

$10000 *Cumulative FV factor @X% for 10 periods = $138164

Cumulative FV factor @X% for 10 periods = $138164/ $10000

Cumulative FV factor @X% for 10 periods = 13.8164

By referring annuity table, this Cumulative FV factor for 10 periods falls at 7%.

therefore X = 7%

Hence third option \"7%\" is correct.