Christopher took a loan of $8,300 from his parents to purchase equipment for his hair salon....

Christopher took a loan of $8,300 from his parents to purchase equipment for his hair salon. They agreed on an interest rate of 3% compounded monthly on the loan. What equal quarterly payments made at the end of each period will settle the loan for 5 years if the first payment is to be made 4 years and 1 quarter from now?

Expert Solution

Quarterly instalment :
Quarterly Instalment is sum of money due as one of several equal payments for loan/ Mortgage taken today, spread over an agreed period of time.

EMI = Loan / PVAF (r%, n)
PVAF = SUm [ PVF(r%, n) ]
PVF(r%, n) = 1 / ( 1 + r)^n
r = Int rate per period
n = No. of periods

How to calculate PVAF using Excel:
=PV(Rate,NPER,-1)
Rate = Disc Rate
NPER = No.of periods

Int rate per quarter = ( 1 + 0.0025)^3 - 1

= 1.0025^3 - 1

= 0.007519

Particulars	Amount
Loan Amount	$ 8,300.00
Int rate per Quarter	0.7519%
No. of Quarters	20

PVAF from 17 to 36 Quarters:

PVAF (0.7519%, 36) = 31.4363

PVAF (0.7519%, 16) = 15.0219

PVAF (0.7519%, 17 to 36) = 16.4144

Equated Quarterly Instalment = Loan Amount / PVAF (r%, n)
Where r is Int rate per Quarter & n is No. of Quarters
= $ 8300 / PVAF (0.0075 , 20)
= $ 8300 / 16.4144
= $ 505.65

Quarterly Instalment is $ 505.65

Pls comment, if any further assistance is required.

jeff jeffy answered 2 years ago

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