Question

6. You loan some money to a friend and he agrees to pay you $200 at the end of each month for the next 2.5 years. Using a rate of 6.3%/year, calculate what this stream of anticipated payments from your friend is worth in today’s dollar terms. In other words, if your friend promises to make these payments, what would be a fair amount to loan to him today?

Answer 1

The fair amount of the loan will be equivalent to the Present value of all the cash stream that will be paid.

Present Value of annuity = P *[(1 - (1+R)^-N)/R]

Where, P = Payment

R = Interest rate per period

N = Number of payments

Number of Payments = 2.5 * 12 [ There are 12 Months in A year]

= 30

Interest rate (Per Month) = 6.3%/12

= 0.525%

So, Present Value of annuity = 200 * [( 1 - (1+0.525%)^-30]/0.525%

= 200 * [( 1 - 1.00525^-30)/0.525%

= 200 * ( 1 - 0.85462884487)/0.00525

= 200 *27.6897438343

= 5537.94876686

So, The Fair amount of loan as on today is $5537.94876686