Answer:
FV = $144,104.88
Explanation:
To determine the amount that Bill will accumulate is the future value of annual amount invested at 12% compounded annually.
The formula for the future value is given below:
The investment:
FV = A× ((1+r)^n - 1)/r
r- 12%, A- 2000, n- 20
FV = 2,000× ((1.12)^20 -1)/0.12
FV = 2000 × 72.05244
FV = $144,104.88
Future value of annuity is the total value of a series of recurring payments at a specified future date. Bill will have $144,104.88 at the end of 20th year.
Future annuity value is the value of repeated payments at a certain future date, deducted a certain refund rate, or a discount rate. The higher the discount rate, the greater the annuity amount.
As per the given information, Future value of annuity is equal to:
[tex]\rm\, FV = A\times \dfrac{[(1+r)^{n} - 1]}{r}\\\\Where, A = Periodic \,Payment\\\\ Rate (r)= Rate\,Per\, period\\\\Number\,of\,Periods (n) = 20[/tex]
[tex]\rm\,FV = 2,000\times \dfrac{[(1+0.12)^{20} - 1]}{0.12}\\\\FV = 2000 \times 72.05244\\\\FV = \$144,104.88[/tex]
Hence, Bill will have $144,104.88 at the end of 20th year.
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