Question

To settle a debt obligation, a person agrees to pay $1,200 at the end of each semi-annual period – the first such payment to be made in 6 months with a total of 23 full payments and a final 24th payment of $950.  If the debt is at j2 = .036, what is the present value of the obligation?

Answer 1

nominal annual interest rate = 0.036

nominal semi-annual interest rate = 0.036/2 = 0.018

Present value of the debt obligation = present value of the first 23 payments + present value of final payment

present value of final payment = final payment / (1+annual interest rate)¹² = 950 / (1+0.036)¹² = 950/ 1.528682

= $621.45

Present value of first 23 payments can be calculated using the PV formula for ordinary annuity

Where C is the periodic payment = $1200

i = semi-annual interest rate = 0.018

n = number of semi annual periods = 23

PV = 1200*18.697824 = $22,437.39

Present value of the debt obligation = present value of the first 23 payments + present value of final payment

= $22,437.39 + $621.45 = $23,058.84