Question

Brian borrows $5,000 from a bank at 8 percent annually compounded interest to be repaid in five annual installments. Calculate the principal paid in the third year.

a. Calculate the​ annual, end-of-year loan payment.

b. Prepare a loan amortization schedule showing the interest and principal breakdown of each of the three loan payments.

Amortization Schedule
End-of-year	Beginning-of-year principle	Loan Payment	Loan Payment		End-of-year balance
			Interest Paid	Principal Paid
1	5,000
2
3

c. Explain why the interest portion of each payment declines with the passage of time.

Answer 1

a. We can use Present value (PV) of an Annuity formula to calculate the annual payment of loan

PV = PMT * [1-(1+i) ^-n)]/i

Where PV of loan = $5,000

PMT = annual payment =?

n = N = number of payments = 5 years

i = I/Y = annual interest rate = 8% per year

Therefore,

$5,000 = PMT* [1- (1+8%) ^-5]/8%

= $1,252.28

The annual, end-of-year loan payment is $1,252.28

b. Amortization schedule

Loan amount	$5,000.0
Annual payment =	$1,252.28
Interest rate =	8%
Time period	5
Amortization Schedule
End-of-year	Beginning-of-year principal	Loan payment (PMT)	Interest Payment @ 8% of beginning balance	Principal payment (Loan Payment - Interest)	End-of-year balance (Beginning balance - Principal Payment)
1	$5,000.0	$1,252.3	$400.00	$852.28	$4,147.72
2	$4,147.72	$1,252.3	$331.82	$920.46	$3,227.25
3	$3,227.25	$1,252.3	$258.18	$994.10	$2,233.15

c. The interest portion of each payment declines with the passage of time because the Beginning-of-year principal amount is reducing with time and with each payment. Therefore 8% interest is charged on lessor amount with the passage of time which reduces the interest portion of each payment.