Question

4)Mario Morales borrowed $ 15,000 at an interest rate of 14% to be paid in 3 years. The loan must be repaid in three equal payments at the end of each year.

a)Calculate the annual payment to be made.

b)Prepare an amortization table that shows the principal and interest payment, as well as the loan balance for each year.

c)Explain why the interest portion of each payment decreases over time.

Answer 1

(a)-Annual end of year loan payment

Loan Amount (P) = $15,000

Annual Interest Rate (r) = 14% per year

Loan Period = 3 Years

Annual Loan Payment = [P x {r (1+r) ⁿ}] / (1 + r) ⁿ – 1

= [$15,000 x {0.14 x (1 + 0.14)³}] / (1 + 0.14)³ - 1

= [$15,000 x {0.14 x 1.48154}] / [1.48154 – 1]

= [$15,000 0.207416] / 0.48154

= $6,460.97 per year

“Annual end of year loan payment = $6,460.97 per year”

(b)-Loan Amortization Schedule

Months	Beginning Loan Amount ($)	Annual Payments ($)	Interest Paid at 14% ($)	Principal Paid ($)	Principal balance remaining ($)
1	15,000.00	6,460.97	2,100.00	4,360.97	10,639.03
2	10,639.03	6,460.97	1,489.46	4,971.51	5,667.52
3	5,667.52	6,460.97	793.45	5,667.52	0.00

(c)- Decline in the interest portion of loan over time

YES. The interest portion of the loan will decrease over time, since the more payments will be made over the life of the loan towards the principal portion. It will result in the reduction of the interest portion of the loan.