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.