A 12-year loan of $144,000 at an effective annual interest rate of 8% is sold af

Question

A 12-year loan of $144,000 at an effective annual interest rate of 8% is sold after four years to an investor. If much the investor should pay for the loan, if: the investor values the loan at an effective annual interest rate of 13%, find how (a) the borrower makes equal annual payments, starting one year after the loan was made; (b) the borrower makes equal annual payments, starting three year after the loan was made; (c) the borrower makes interest-only payments annually, and a lump sum principal payment at the end; (d) the borrower makes level payments of principal annually, starting one year after the loan was made. Hint: Break down the loan as a sum of loans and use Makeham's Formula.]

Explanation / Answer

Time period = 12 years

Loan Principal = $144,000

Effective interest rate = 8% p.a

Total interest for 12 years = P*T*R /100 = $144,000 * 12 * .08 = $138,240

Total amount to be repaid = Principal + Interest = $ (144,000 + 138,240)= $282,240

(a) Borrower makes equal payments after one year the loan was made, so the total amount repaid by the borrower in four years should be calculated :

Each year repayment made by the borrower =Total amount /12 = $(282,240/12) = $ 23,520

so for four years total repayment made = $ 23,520 * 4 = $94,080

Remaining amount with the borrower from the loan = $(144,000-94,080) = $49,920

SO borrower can lend $49,920 to the investor for 13% interest

So the interest paid by the investor = P * T * R/100 = 49,920 * 8 * 0.13 = $51,916.8

so the total amount repaid by the investor = $(49,920 + 51,916.8) = $ 101,836.8

(b) The borrower starts paying three years after the loan was made, so he pay annual equal payments for the last 9 years.

so the total amount paid each year after three years = $ (282,240 /9) =$31,360

So for third and fourth year borrower pays $(31,360 * 2 ) =$62,720

So the loan amount left with the borrower = $(144,000 - 62,720) = $81,280

So the investor takes this $81,280

Total interest paid by the investor = P*T*R/100 = $81,280 * 8 *0.13 = $84,531.2

Total amount paid by the investor = Principal + Interest = $(81,280 + 84,531.2) = $165,811.2

(c)Interest payments annually made by the borrower = P * R/100 = 144,000 * 0.08 = $11,520

Total interest paid for four years = $11,520 * 4 =$46,080

So the remaining loan amount with the borrower = $(144,000 - 46,080) = $97,920

Investor takes amount $97,920

Total interest paid by the investor = P*T*R/100 = $ 97,920 * 8 *0.13 = $101,836.8

TOtal amount repaid by the investor = $(97,920 + 101,836.8) = $199,756.8

(d) The borrower pay level payments of principal annually ,that is =$(144,000/12) = $12,000

Total amount paid in 4 years = $12,000 * 4 =$48,000

So the amount left with the borrower = $(144,000-48,000)=$96,000

SO the investor takes Principal =$96,000

Total interest paid by the investor = P*T*R /100 = $96,000 * 8 * 0.13 = $99,840

Total amount repaid by the investor = Principal + Interest = $(96,000 + 99,840) = $ 195,840

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