Question

Problem #5: A loan of $60,000 is paid off in 36 payments at the end of each month in the following way: Payments of $1500 are made at the end of the month for the first 12 months. Payments of $1500 + x are made at the end of the month for the second 12 months. Payments of $1500 + 2x are made at the end of the month for the last 12 months. What should x be if the nominal monthly rate is 11.6%? Problem #5: Answer correct to 2 decimals.

Answer 1

Since 60,000 is paid every through 36 installment every .

First finding the present value of first 12 payments of $1500

PV = PMT * (1-(1/(1+r)^n))/r

PMT = 1500

= 1500 * (1-(1/(1+0.116)^12))/(0.116)

=9466.3

Calculating PV of 1500 +2x payments made for the second 12 months. We will find PV of payments at the end of first 12 months and then discount it to find PV today.

PMT = 1500 + x

PV at end of first 12 months = (1500 + x)* (1-(1/(1+0.116)^12))/(0.116) = 9466.3 + 6.31 x

PV of these payments today = (9466.3 + 6.31x)/(1.116)^12 = 2536.36 + 1.69 x

Find PV of Payments received for last 12 months

PMT = 1500 +2x

Calculating PV at the end of 24 months = (1500+2x)*(1-(1/(1+0.116)^12))/(0.116) = 9466.35 + 12.62 x

Calculating PV today = ( 9466.3 + 12.62 x)/(1.116)^24 = 679.57 + 0.91 x

Finding Value of X

60,000 = 9466.35 + 2536.36 + 1.69 x + 679.58 + 0.91 x

60,000 = 12682.29 + 2.6 x

x = 18199.12