It is now the beginning of the year (year 0). Assume that, starting at the end of the year 4 (NOT next year), you will make deposits of $643 each year into a savings account. You will make a total of 7 annual deposits. If the savings account interest rate is 13%, what is the present value of this savings plan? Enter your answer in dollars, rounded to the nearest cent.
Answer:
Present Value = = $1,970.85
Working notes for the above answer is as under
We have been provided with the information that,
you will make deposits of $643 each year into a savings account. You will make a total of 7 annual deposits.
The payment will start at the year 4
So first of all we will calculate Future value at the year 13 as follow
| Year | Deposit | FV factor at 13% |
Future Value |
| 0 | 0 | ||
| 1 | 0 | 0 | |
| 2 | 0 | 0 | |
| 3 | 0 | 0 | |
| 4 | 643 | 2.081952 | 1338.695 |
| 5 | 643 | 1.842435 | 1184.686 |
| 6 | 643 | 1.630474 | 1048.395 |
| 7 | 643 | 1.442897 | 927.7828 |
| 8 | 643 | 1.2769 | 821.0467 |
| 9 | 643 | 1.13 | 726.59 |
| 10 | 643 | 1 | 643 |
| Total | 6690.195 |
So at the year end 10 he will have $ 6690.195 and now find the present value of such $ 6690.195 as follow
Present Value
=6690.195 x PVIF (13%,year 10)
=6910.195 x 0.2946
= $1,970.85
