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I am trying to solve the following problem and I am not quite sure what it means.

A loan of 100,000 is payable over five years with monthly payments of 60,000 commencing one month after the inception date. The loan repayment is 2,000 per month and the nominal rate 10 percent. How much capital remains at the end of five years?

I am not quite understanding the vocabulary here.

I understand that the effective monthly rate is $i =10/12$% and it is an annuity immediate problem.

So the future value can be calculated as

$$FV = 2000s_{{\over{60|}i}}$$

But I am not understanding the meaning of "payable" and "monthly payments of 60000"

Is 100000 the total capital of how much the person is borrowing or is it the interest of what needs to be paid, or something else?

Can I get some help?

hyg17
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  • The problem is unclear. I'd normally have read the first clause as stating that the entire loan had to be paid off in five years, but what follows appears to contradict that. My best guess: $100K$ is borrowed for an unstated time (not less than five years). It is paid on an amortizing schedule, like a mortgage. We know the level coupon. We know the implied interest rate. Determine the final maturity and the remaining balance after 5 years. Not sure what "monthly payments of $60K$" might mean. – lulu Apr 23 '16 at 19:50
  • If I use your idea 100K is 164530 in 5yrs and the payment adds up to 154874 at the end of 5 yrs so it clearly seems that the loan was not paid off. But the 60K throws me off, too. – hyg17 Apr 23 '16 at 20:24
  • That "monthly payments of $60K$" is truly weird. Could that be the total interest paid over the life of the loan? Anyway, I'd have thought there was enough information to analyze the loan even without understanding what this clause might mean. – lulu Apr 23 '16 at 20:26
  • I looked at the answer and the number that they are looking for itself indeed is $$100K(1+i)^{60} - 2K \frac{(1+i)^{60}-1}i = 94,130 $$. I do want to understand what the 60K was, though... can anyone answer that? – hyg17 Apr 23 '16 at 20:37
  • @hyg17 The 60,000 is irrelevant to the question. Basically, you have a loan that you're taking out that you won't get the entire value out immediately as a lump sum - you receive the loan as the annuity. Since you're calculating the current value of the loan at 5 years (Loan Payments - how much you've paid), the 60,000 is irrelevant, as by the time you've hit 5 years, you've already received the amount of the entire loan. Let me know if you have any questions. If you were looking at the current value at some period before five years, you would have to take into account how many payments of... – Clarinetist May 02 '16 at 17:15
  • @hyg17 60,000 you have before the time you are interested in, and compute the future value appropriately. – Clarinetist May 02 '16 at 17:15
  • @hyg17 To see why this works out mathematically, obviously, the payments of 60,000 have a present value of 100,000. Move this value on its own up five years, and you will have the current value of the payments of 60,000 at five years after the inception of the loan. Alternatively, you could take the future value of each payment calculated at 60 months, but you would have to do it for each payment at 1 month, 2 months, ...., 60 months. They should turn out to be the same number. – Clarinetist May 02 '16 at 17:19

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