Question

Quantum Pizza took out a loan from the bank today for 21,000 dollars. The loan requires Quantum Pizza to make a special payment of 13,700 dollars to the bank in 5 years and also make regular, fixed payments of X to the bank each year forever. The interest rate on the loan is 7.86 percent per year and the first regular, fixed annual payment of X will be made to the bank in 1 year. What is X, the amount of the regular, fixed annual payment?

the first step is 13,700 dived by (1.0786)^5 then after than that result we will added to 21,000 then we will mutply by (1.0786) but still I got this wrong can you helped me out

Answer 1

Loan amount = $21000

forever payment of X each at the end of every year and 1 payment after 5 year of $ 13700.

r = 7.86%

So let us first calculate PV of $13700

PV = FV/(1+r)^t = $13700/(1.0786^5) = $9384.66

Subtracting it from 21000 to calculate remaining amount = 21000-9384.66 = $11615.34

So now, 11615.34 = X/1.0786 + X/ 1.0786^2 + X/1.0786^3....

using Sum of a infinite GP Sum = a/(1-r), here a = X/1.0786, r = 1/1.0786

So, 11615.34 = (X/1.0786)/(1 - 1/1.0786)

So, X = $912.97 or $913