Question

Home loans typically involve "points," which are fees charged by the lender. Each point charged means that the borrower must pay 1% of the loan amount as a fee. For example, if the loan is for $100,000 and 2 points are charged, the loan repayment schedule is calculated on a $100,000 loan but the net amount the borrower receives is only $98,000. Assume the interest rate is 1% per month. What is the effective annual interest rate charged on such a loan, assuming loan repayment occurs over 360 months? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Use a financial calculator or Excel.)

Answer 1

Answer:

Ans. The effective annual interest rate charged on the loan is 12.99% effective annually. (Please see the attached excel spread sheet)

Explanation:

Hi, attached is the amortization table that I made for this case. Notice that there is a yellow and green cell, the yellow one is the result of using the "IRR" function of MS Excel which provides an effective monthly rate, since the payments are made every month, then we have to transform that monthly effective rate into an effective annual rate, this is the formula to use.

$EffectiveAnnual=(1+EffectiveMonthly)^{\frac{1}{12} } -1$

That is:

$EffectiveAnnual=(1+0.012267477)^{\frac{1}{12} } -1=0.12986448$

Which we round to 12.99% effective annually.

Finally, notice that I didnt use the payments to find the effective rate, I used the cash flow, that was because you didn´t receive all the 100K (the fee, remember?), you received $98,000.

Best of luck.

Answer 2

Answer:

Ans. The effective annual interest rate charged on the loan is 12.99% effective annually. (Please see the attached excel spread sheet)

Explanation:

Hi, attached is the amortization table that I made for this case. Notice that there is a yellow and green cell, the yellow one is the result of using the "IRR" function of MS Excel which provides an effective monthly rate, since the payments are made every month, then we have to transform that monthly effective rate into an effective annual rate, this is the formula to use.

That is:

Which we round to 12.99% effective annually.

Finally, notice that I didnt use the payments to find the effective rate, I used the cash flow, that was because you didn´t receive all the 100K (the fee, remember?), you received $98,000.