Assume annual payments of 6318 for 3 years and an interest r

Assume annual payments of $6318 for 3 years and an interest rate of 6.9% per year. What initial principal (present value) will this repay?

Solution

Present value = P [ {1 - (1+r)^-n} / r ]

Here, P = periodic payment = $ 6318

n = no. Of periods = 3

r = rate per period = 6.9? = 0.069

Therefore, Present value = 6318 [ {1 - (1+0.069)^-3}/0.069] = 6318 [ {1 - (1/(1.069)³)}/0.069] = 6318 [ {1 - ( 0.81859)}/0.069] = 6318 (0.18141/0.069) = (6318 * 2.62913) = $16,610.8

Answer- $ 16,610.8