A church congregation has raised $37,625 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?
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Part 1
The size of the payment is $
enter your response here.
(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)
To calculate the annual payment that can be made for ten years:
1. Calculate the future value of the investment after 4 years:
PV = $37,625
r = 0.07 (7% annual interest rate)
n = 4 (compounded quarterly)
FV = PV * (1 + r/n)^(n*t)
FV = $37,625 * (1 + 0.07/4)^(4*4)
FV = $37,625 * (1 + 0.0175)^16
FV = $37,625 * (1.0175)^16
FV = $37,625 * 1.300628
FV = $48,970.98
2. Calculate the annuity payment using the future value as the present value for an ordinary annuity formula:
PV = $48,970.98
r = 0.07
n = 4
t = 6 (10 years - 4 years)
Annuity Payment = PV * (r/n) / [(1 - (1 + r/n)^(-n*t))]
Annuity Payment = $48,970.98 * (0.07/4) / [1 - (1 + 0.07/4)^(-4*6)]
Annuity Payment = $48,970.98 * 0.0175 / [1 - (1.0175)^(-24)]
Annuity Payment = $48,970.98 * 0.0175 / [1 - 0.606101]
Annuity Payment = $48,970.98 * 0.0175 / 0.393899
Annuity Payment = $855.20
Therefore, the annual payment that can be made for ten years from the fund is $855.20.