A mortgage has a yearly nominal interest rate of 6 percent. It is repaid in equa

Question

A mortgage has a yearly nominal interest rate of 6 percent. It is repaid in equal monthly payments of $1716.16

Each payment of the mortgage has 2 parts: the principal and the interest. The second mortgage payment had -for the interest part – an amount of $823.

How much was the loan, and how many years was the loan taken for?

I know the answer is supposed to be:

* the amount of the loan was $165,540

* the period of the loan was 11 years

I don't understand how they arrived at this answer.

Please help. Thank you.

Explanation / Answer

let loan be $ a and tenure be n years i.e. 12n months Interest rate = 6% = 0.06 Monthly rate = 0.06/12 = 0.005 At year 1, Interest = 0.005 a ($) Principal paid = 1716.16 - 0.005a ($) Principal due = a - (1716.16 - 0.005a) = 1.005 a - 1716.16 ($) At year 2, Interest = 0.005(1.005 a - 1716.16) = 823 (given) => a = 165488.7 ($) (ANSWER) PV of monthly cash flows = c ((1+k)^p -1)/(k(1+k)^p) (where, c = monthly cash flow = 1716.16, k = monthly rate = 0.005, p = period in months = 12*n) So, PV = a = 165488.7 = 1716.16(1.005^(12*n) -1)/(0.005*1.005^(12*n)) => n = 10.995 = say 11 years (ANSWER)

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