Lionel’s student loan of $21,500 at 3.92% compounded quarterly was amortized over 4 years with payments...

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

Expert Solution

$ 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

jeff jeffy answered 1 year ago

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