Question

Asked Jun 21, 2019

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You borrowed $700 at 5% compounded quarterly. Your

payments are $150 at the end of each year. How many years will you make payments on the loan?

(Hint: compounding frequency is different from payment frequency; we know that r and t should be matched; compounding effect? Effective interest rate?)

Step 1

We will adopt the following approach:

- It's a typical time value of money case, where we have to find nper i.e. net period the loan will remain outstanding under annual payment.
- However, there is one small catch. he payment frequency is annual. Hence the period here is 1 year. However the interest is getting compounded quarterly. Henece, we need to calculate the interest rate per period i.e. interest rate per annuam i.e. the effective annual rate (EAR).
- EAR will match the interest rate and the frequency of payment to annual basis
- After that we will use the NPER function of excel to get the number of years the loan will remain outstanding.

Step 2

Inputs of NPER function:

PV of loan = - Borrwed amount = - $ 700

Rate = EAR = (1 + 5% / 4)^{4} - 1 = 5.09%

PMT = Payment per period = $ 150

FV = Future value = 0

Step 3

Please see the table on the white board for calculation of total period of loan using NPER function of excel.The last row highlighted in yel...

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