Question

# Ricky borrows X amount for 30 years at nominal rate of 12% compounded monthly from BANKFB....

Ricky borrows X amount for 30 years at nominal rate of 12% compounded monthly from BANKFB. If he pays the principal as equal monthly installments for 30 years and on top of this payment, he pays every month the interest on the outstanding balance. Immediate after 200th payment, the BANK FB sells the contract on the future payments to BANK SD at a price of 102,891.65. Find the value of the initial loan amount X.

Solution :-

Total Term of Loan = 30 Years = ( 30 * 12 ) = 360 monthly Payments

Interest Rate per month = 12% / 12 = 1%

Now Loan Balance after 200 Payments = 102,891.65

Installment remaining = 360 - 200 = 160

Let Value of each installment be Y

Now 102,891.65 = Y * PVAF ( 1% , 160 )

Y = 102,891.65 / 79.6493 = \$1,291.81

Therefore Value of each Installment = \$1,291.81

Now Value of Initial Loan = Present Value of 360 Payments

= \$1,291.81 * PVAF( 1% , 360 )

= \$1,291.81 * 97.21833

= \$125,587.61

Therefore the initial loan amount = \$125,587.61

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