Question

Cathy Cortez-Ochoa borrowed $4,000 from her uncle who amortized the loan at 4.5% over 3 months. Use the table below: the first two monthly payments are $1,343.35 each. (The last payment may be slightly different). Complete the amortization schedule and solve the effective rate problem.

Amortization Payment Factors per $1,000 Borrowed
Amount of Monthly Payment per $1,000 Borrowed
	Term of Loan	Annual Interest Rate
		4.5%	6%	7.5%	9%	10.5%	12%
1	month	1003.75000	1005.00000	1006.25000	1007.50000	1008.75000	1010.00000
2	months	502.81425	503.75312	504.69237	505.63200	506.57203	507.51244
3	months	335.83645	336.67221	337.50865	338.34579	339.18361	340.02211
4	months	252.34814	253.13279	253.91842	254.70501	255.49257	256.28109
5	months	202.25561	203.00997	203.76558	204.52242	205.28049	206.03980
6	months	168.86099	169.59546	170.33143	171.06891	171.80789	172.54837
1	year	85.37852	86.06643	86.75742	87.45148	88.14860	88.84879
2	years	43.64781	44.32061	44.99959	45.68474	46.37604	47.07347
3	years	29.74692	30.42194	31.10622	31.79973	32.50244	33.21431
4	years	22.80349	23.48503	24.17890	24.88504	25.60338	26.33384
5	years	18.64302	19.33280	20.03795	20.75836	21.49390	22.24445
10	years	10.36384	11.10205	11.87018	12.66758	13.49350	14.34709
15	years	7.64993	8.43857	9.27012	10.14267	11.05399	12.00168
20	years	6.32649	7.16431	8.05593	8.99726	9.98380	11.01086
25	years	5.55832	6.44301	7.38991	8.39196	9.44182	10.53224
30	years	5.06685	5.99551	6.99215	8.04623	9.14739	10.28613

	Month	Unpaid Balance	Interest Payment	Total Payment	Principal Payment	New Balance
a.	1
b.	2
c.	3
d.	Use the amortization schedule to compute the effective annual interest rate where P is the average principal over the 3-months and I is the total interest charged.
	Principal	Interest	Rate

Answer 1

Yearly interest rate = 4.5%

Monthly interest rate = 4.5/12

= 0.375%

Monthly installment = 4000/PVIFA(0.375%,3)

=4000/2.97764

= 1343.35

Amortization table of the loan will be as follows -

	Unpaid balance	Interest payment (Unpaid bal.*monthly int. rate)	Total Payment	Principal Payment (Total payment - Int. amt)	New balance
1	4000.00	15.00	1343.35	1328.35	2671.65
2	2671.65	10.02	1343.35	1333.33	1338.32
3	1338.32	5.02	1343.34	1338.32	0.00

(d) Effective annual interet rate = (1+nominal monthly interest rate)^12 - 1

nominal monthly interest rate = 4.5/12 = 0.375%

so Effective monthly interest rate = (1+0.00375)^12 - 1

= (1.00375)^12 - 1

= 1.04594 - 1

= 0.04594 or 4.594%

Effective yearly interest rate = 4.594%

Please check with your answer and let me know.