Question

Please show the works

P5-48 Loan amortization schedule Joan Messineo borrowed $45,000 at a 4% annual rate of interest that she must repay over 3 years. The loan is amortized into three equal, end-of-year payments. a. Calculate the end-of-year loan payment. b. Prepare a loan amortization schedule showing the interest and principal break- down of each of the three loan payments. c. Explain why the interest portion of each payment declines with the passage of time.

Answer 1

Loan Amount	45,000
Rate	4%
Loan Term	3 Years
Answer to (b)
Loan Amortization Schedule	A	B	C = A*4%	D = (B-C)	E = (A-D)
Year	Beginning Balance	Annual Repayment (Refer WN-1)	Interest @ 4%	Pricipal Paid	Closing Balance
1	45,000	16,216	1,800	14,416	30,584
2	30,584	16,216	1,223	14,992	15,592
3	15,592	16,216	624	15,592	-
WN-1
Calculation of Annual Repayments
Annual repayment * sum of PV factor=	$      45,000
Annual repayment * 2.77509103322713 =	$      45,000
Annual repayment =	$      45,000 /2.77509103322713
Annual repayment =	16,216
PV Factor = 1/(1+r)^n
where : r = rate of interest , n = time
PV Factor @ 4% for	Apply formula	PV is
1	1/(1+0.04)^1	0.961538462
2	1/(1+0.04)^2	0.924556213
3	1/(1+0.04)^3	0.888996359
Sum of PV Factors		2.775091033
a)
The end of year loan payment is $ 16,216
b) Explained above
c)
With every passing year the interest portion declines as the principal gets reduced and hence interest gets reduced in subsequent payments and repayment of principal gets
increasing.