Question

After having analyzed the real interests that are charged in different commercial establishments, a person has decided to dedicate himself to a lender. For this, he will establish the company called "The Last Resort". In this company, the way of operating is as follows: When a person applies for a loan of $ P, this amount will be transferred at the end of the term contained in years, according to the expression: F = P (F / P, 10%, n).
Subsequently, to determine the size of the annual payments, the amount F is divided by the number of years covered by the loan. If a person applies to this company for a $ P loan for a period of 5 years, what would be the annual real interest that results from this transaction?

Answer 1

Let the loan amount ($P) = $100

Therefore, the future value (F) at the interest rate (r) of 0.10 for the number of years (n) of 5 is as below:

F = P × (1 + r) ^n

    = 100 × (1 + 0.10) ^5

    = 100 × (1.10) ^5

    = 100 × 1.61051

    = 161.051

(Or)

F = P (F / P, 10%, n)

   = 100 × 1.61051 [from the factor table of (F/P) at 10% rate for 5 year]

   = 161.051

Annual payment = F / n

                            = $161.051 / 5

                            = $32.2102