Question

1.

Find the present value.
Amount per Payment: $820

Payment at the End of Each: 6 months

Number of Years: 14

Interest Rate: 5%

Compounded: Semiannually

Answer 1

The amortization formula applies.
A = P*(r/n)/(1 -(1 +r/n)^-(nt))
where
A is the payment in each compounding period (820)
P is the principal amount (present value)
r is the annual interest rate (.05)
n is the number of compoundings per year (2)
t is the number of years (14)

Filling in the numbers, we have
820 = P*(.05/2)/(1 -(1 +.05/2)^-(2*14))
820 = .025P/(1 -1.025^-28)
P = 820(1 -1.025^-28)/.025
P ≈ 16,371.21

The present value of that string of payments is $16,371.21.