Question

Lionel’s student loan of $21,500 at 3.92% compounded quarterly was amortized over 4 years with payments made at the end of every month. What was the principal balance on the loan after 3 years?

Round to the nearest cent

Answer 1

$ 5,693.48

Step-1:Calculation of equivalent monthly interest rate
(1+i1)^n1	=	(1+i2)^n2		Where,
(1+i1)^3	=	(1+0.0098)^1	i2	=	Quarterly Interest rate
(1+i1)^3	=	1.0098			=	3.92%/4
1+i1	=	1.0098	^(1/3)		=	0.0098
1+i1	=	1.003256
i1	=	0.003256		i1	=	Monthly Interest rate	=	?
				n1	=	Month in a quarter	=	3
				n2	=	Quarter in a quarter	=	1
Step-2:Calculation of monthly payment
Monthly Payment	=-pmt(rate,nper,pv,fv)	Where,
	$     484.56			rate	=	0.00325605
				nper	=	48
				pv	=	$       21,500
				fv	=	0
Step-3:Loan balance after 3 years
Loan balance after 3 years	=pv(rate,nper,pmt,fv)	Where,
	= $ 5,693.48			rate	=	0.00325605
				nper	=	12
				pmt	=	$     -484.56
				fv	=	0