Question

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?

Answer 1

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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