Question

Joan Messineo borrowed ?$19,000 at a 9?% annual rate of interest to be repaid over 3 years. The loan is amortized into three? equal, annual,? end-of-year payments.

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

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

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

Answer 1

a. Amount borrowed = $19,000. Annual rate = 9% and n = 3. Using the "PMT" function in excel, the annual payments will be = PMT(9%, 3, 19,000). This will give us a reult of $7,506.04

Alternatively the formula can be used: Annual payment = [P x R x (1+R)^N]/[(1+R)^N-1]

= [19,000*9%*(1.09)^3]/[(1.09^3)-1]

= 2214.50/0.30

= $7,506.04

b. Loan amortization table:

	Amount due at the beginning of the period	Annual payment	Interest	Principal repayment	Amount due at the end of the period
Year
1	19,000.00	7,506.04	1,710.00	5,796.04	13,203.96
2	13,203.96	7,506.04	1,188.36	6,317.68	6,886.28
3	6,886.28	7,506.04	619.76	6,886.28	0.00

Calculations and explanations:

Interest amount in year 1 = 9% of 19,000 = $1710. Principal repayment = 7506.04 - 1710 = 5796.04. Thus amount of principal due at the end of year 1 = 19000-5796.04 = $13203.96. Similarly figures have been computed for years 2 and 3.

c. Interest portion of each payment declines with the passage of time as the amount of principal due declines in each year. Each year your payment is servicing the principal loan (besides paying interest) and so the amount due at the beginning of a period keeps on declining each year. This leads to decline in interest portion as: interest portion = 9% * amount of principal due, and amount of principal due keeps on declining each year.