Chad borrows $75,000 and agrees to repay the loan in five equal annual installments. The loan's...

Chad borrows $75,000 and agrees to repay the loan in five equal annual installments. The loan's interest rate is 6.75 percent. What is his loan's balance after making the third payment?

Expert Solution

Yearly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]

Using the formula:
Loan amount	P	$ 75,000

Rate of interest per period:
Annual rate of interest		6.750%
Frequency of payment	=	Once in 12 month period
Numer of payments in a year	=	12/12 =	1
Rate of interest per period	R	0.0675 /1 =	6.7500%

Total number of payments:
Frequency of payment	=	Once in 12 month period
Number of years of loan repayment	=	5.00
Total number of payments	N	5 × 1 =	5

Period payment using the formula	=	[ 75000 × 0.0675 × (1+0.0675)^5] / [(1+0.0675 ^5 -1]
Yearly payment	=	$ 18,169.53

Loan balance	=	PV * (1+r)^n - P[(1+r)^n-1]/r

Loan amount	PV =	75,000.00

Rate of interest	r=	6.7500%
nth payment	n=	3
Payment	P=	18,169.53

Loan balance	=	75000(1+0.0675)^3 - 18169.53[(1+0.0675)^3-1]/0.0675
Loan balance	=	32,965.02

Answer is $32,965.02

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jeff jeffy answered 1 year ago

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