A church congregation has raised $37 comma 625 for future outreach work. If the money is invested in a fund paying 7% compounded quarterly, what annual payment can be made for ten years from the fund if the first payment is to be made four years from the date of investment in the fund?
Part 1
The size of the payment is $
(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)
To calculate the size of the annual payment that can be made for ten years from the fund, we can use the formula for the future value of an annuity:
FV = Pmt * ((1 - (1 + r)^-n) / r)
Where:
FV = Future value of the annuity ($37,625)
Pmt = Annual payment
r = Quarterly interest rate = 0.07/4 = 0.0175
n = Number of quarters from the first payment to the end of ten years = 10 * 4 = 40
Substitute the values into the formula:
37625 = Pmt * ((1 - (1 + 0.0175)^-40) / 0.0175)
Solve for Pmt:
37625 = Pmt * ((1 - (1.0175)^-40) / 0.0175)
37625 = Pmt * ((1 - 0.572597) / 0.0175)
37625 = Pmt * (0.427403 / 0.0175)
37625 = Pmt * 24.457
Pmt = 37625 / 24.457
Pmt ≈ $1538.47
Therefore, the annual payment that can be made for ten years from the fund is approximately $1538.47.