a question for Mr. Cherry.

[audia4]

Hello. Could you tell me how to approach this question.

Question:

Jeff obtains a mortgage loan of 55,000 to be repaid with monthly payments at the end of each month over n years. Each monthly payment is 500.38, based on a nominal interest rate of i compounded monthly, i >0. Jef is unable to make the first payment but makes all the other paymetns on time. Still, because he skipped the first payment, he owes 3077.94 at the end of n years. Calculate i.

Why is the following incorrect.

55,000(1+i^12/12) + 3077.94 = 500.38s_n-1. Essentially, what I am thinking is that after one time period, 55,000 will grow with interest to 55,000(1+i^12/12), whic along with the 3077.94 must balance the present value of the remaining payments.

Thank you.

[PistolPt01]

This one kind of blew my mind too. It was here I stopped with the questions from 6a and moved on. Its been smooth sailing ever since :)

[SCIGEEK]

Hello. Could you tell me how to approach this question.

Question:

Jeff obtains a mortgage loan of 55,000 to be repaid with monthly payments at the end of each month over n years. Each monthly payment is 500.38, based on a nominal interest rate of i compounded monthly, i >0. Jef is unable to make the first payment but makes all the other paymetns on time. Still, because he skipped the first payment, he owes 3077.94 at the end of n years. Calculate i.

Why is the following incorrect.

55,000(1+i^12/12) + 3077.94 = 500.38s_n-1. Essentially, what I am thinking is that after one time period, 55,000 will grow with interest to 55,000(1+i^12/12), whic along with the 3077.94 must balance the present value of the remaining payments.

Thank you.

I don't understand the notation (1+i^12/12). Shouldn't it be (1+i/12)^12 ?
Also, if you are writting the equation after the end of the first year, then you have to consider the value of 3077.94 at that point of time and also the value of the annuity at that point of time and not at the end of n years.

Here is what I think should be true:

Let j be the effective rate of interest, i.e j = i/12

So, the future value of the annuity of 500.38 over a (12n-1) payment peroids is not enough to pay off the loan. He still needs to make a payment of 3077.94 to pay it off.
So, the total payment he will need to make at the end of n years ( or 12n pay periods) is

500.38s_(12n-1) + 3077.94 and this amount must be equal to the accumulated value of 55000 at an effective rate of j over 12n pay periods. So the equation should be

55000(1+j)^(12n) = 500.38s_(12n-1)+3077.94

[Harold Cherry]

SCIGEEK's equation looks correct to me.