Question

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?)

Answer 1

- Present value of borrowed amount = $700

- Periodic annual payment at the end of each year = $150

Interesr rate = 5% compounded quarterly

calculating Effective Annual rate of compounded quarterly:-

Where,

r = Interest rate = 5%

m = no of times compounding in a year = 4 (compounded Quarterly)

EAR = 1.050945 - 1

EAR = 5.0945%

Now, Calculating the number of years to pay back the loan using PV of annuity formula:-

Where, C= Periodic Payments = $150

r = Periodic Interest rate = 5.0945%

n= no of periods

Preseent value = $700

Taking log on both sides,

-n*Log(1.050945) = Log(0.76225666667)

-n*0.0215800 = -0.11789877

n = 5.46 years

So, years will you make payments on the loan is 5.46 years

If you need any clarification, you can ask in comments.    

If you like my answer, then please up-vote as it will be motivating