b. Ben took up a loan to purchase a farm machine. The terms of his loan...

b. Ben took up a loan to purchase a farm machine. The terms of his loan require him to make quarterly payments of $3,434 over 7 years. The relevant rate of interest is 7.2% per year, compounded quarterly. For the same amount of loan and interest rate, will Ben pay off the loan sooner if he makes quarterly payments of $3,876 instead? Show all relevant calculations to support your answer.

Expert Solution

First, lets find out the loan amount.

Loan amount would be present value of all quarterly payments discounted @7.2% per year

Assuming installments are paid at end of quarter
Installment	$ 3,434.00
No. of period (7*4)	28
Rate (7.2/4)	1.80%
PV formula in excel	=PV(rate,nper,pmt,fv,type)
PV	=PV(0.018,28,-3434,,0)
	$75,009.39

Now considering PV as the amount of loan, find out the number of installments when installment amount is $ 3876

nper formula in excel	=nper(rate,pmy,pv,fv,type)
nper	=NPER(0.018,3876,-75009,,0)
nper	24.00407906

This shows 24 installments
4 installments in one years bring it to a total of 6 years
Hence, the loan can be re-paid in 6 years

Considering rounding of factor, if we consider the loan amount to be exact $ 75000, then also it come out to be 24 installments

nper formula in excel	=nper(rate,pmy,pv,fv,type)
nper	=NPER(0.018,3876,-75000,,0)
nper	24.00048403

ekkarill92 answered 2 hours ago

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