# math

posted by
**john** on
.

find the present value of ordinary annuity

payments of 890 each year for 16 years at 8% compounded annually

What is the amount that must be paid (Present Value) for an annuity with a periodic payment of R dollars to be made at the end of each year for N years, at an interest rate of I% compounded annually?

For this scenario, P = R[1 - (1 + i)^(-n)]/i where P = the Present Value, R = the periodic payment, n = the number of payment periods, and i = I/100.

Example: What is the present value of an annuity that must pay out $12,000 per year for 20 years with an annual interest rate of 6%? Here, R = 12,000, n = 20, and i = .06 resulting in

P = 12000[1 - (1.06)^-20]/.06 = $137,639

Therefore, the purchase of an annuity bearing an annual interest of 6% for $137, 639, will anable the $12,000 annual payment over a 20 year period, for a total payout of $240,000.