Question

Let us say Texas Community Bank made a loan of $2000 to Taco Palenque at a rate of 10% per year. The loan is to be paid in installments in 5 years- one installment per year.

a) This means that taco palenque is expected to make equal payments of how much every year for 5 years?

b) If after two years, TCB wants to sell the loan to a third party, how much is it likely to sell for?

Answer 1

Loan Amount = $2,000 = P = 2,000

Rate of interest = 10% = r = 10/100 = 0.10

Term of the loan = 5 years = n = 5

a) Payment Required at the end of each year will be calculated using the following formula

Payment = P (r(1+r)^n)/((1+r)^n-1)

= 2,000 * (0.10 * (1 + 0.10)^5 ) / ((1 + 0.10) ^5 - 1 )

= 2,000 * ( 0.10 * 1.1^5) / (1.1^5 - 1)

= 2,000 * 0.161051 / 0.61051

= $527.60 => Answer

b) Value of loan after two years can be calculated using NPV (Net Present Value) method for the expected cash flow

Value of Loan = 527.6 /(1 + 0.10) ^1 + 527.6 /(1 + 0.10) ^2 + 527.6 /(1 + 0.10) ^3

= 527.6/1.1 + 527.6 / 1.21 + 527.6 / 1.331

= 479.64 + 436.03 + 396.39

= $1312.06 => Answer