Question

Tanya is selling her old car for $6,933. If a prospective buyer offers to make yearly payments for the next 5 years, what should Tanya set these payments to if the correct discount rate is 0.11?

Answer 1

Value of car =  P = $6933

Interest Rate = r = 0.11

Number of payment periods = n = 5

Let annual payments made be X

Hence, the sum of present value of annual payments must be equal to the value of the loan amount

=> X/(1+r) + X/(1+r)² +....+ X/(1+r)^N = P

=> X[1- (1+r)^-N]/r = P

=> X = rP(1+r)^N/[(1+r)^N-1]

Hence, MoAnnualnthly Payments =  rP(1+r)^N/[(1+r)^N-1]

= 6933*( 0.11)*(1+ 0.11)⁵/((1+ 0.11)⁵-1) = $1875.86