Question

1. What linear gradient amount beginning in period 2 is required so that a loan of 12,000 is paid off in 8 periods using an interest rate of 8.00% if the beginning loan payment one period from now is 1900? Clearly indicate the sign of the gradient in your answer.

Answer 1

Let G be the linear gradient.

First payment=$1900

Rate of interest=i=8%

Number of periods=n=8

PW of future payments=1900*(P/A,8%,8)+G*(P/G,8%,8)

We need the value of present value factors. Present value factors can be calculated as

PW of future payments=1900*(P/A,8%,8)+G*(P/G,8%,8)

PW of future payments is equal to the loan amount which is $12000

12000=1900*5.746639+17.806098*G

G=(12000-1900*5.746639)/17.806098=60.73

Linear gradient amount starting in 2nd year is $60.73