Question

Amortization.  Loan Consolidated Incorporated​ (LCI) is offering a special​ one-time package to reduce Custom​ Autos' outstanding bills to one​ easy-to-handle payment plan. LCI will pay off the current outstanding bills of $234,000 for Custom Autos if Custom Autos will make an annual payment to LCI at an interest rate of 12​% over the next 5 years.  

a.  What are the annual payments of the​ loan?

b.  What is the amortization schedule for this loan if Custom Autos wants to pay off the loan before the loan maturity in 5 ​years?

c.  When will the balance be half paid​ off?  

d.  What is the total interest expense on the loan over the 5 ​years?

Answer 1

a) To find the annual payment of loan, we can use present value of annuity formula:

Where,
PVA = Present Value of Annuity / Loan amount
A = Annuity / Payment
i = rate of interest
n = number of years

Therefore, annual payment = $64,913.88

b) Amortization Table.

Here, Interest part = Opening balance * Interest Rate

Principal part = Annual payment - Interest part.

Year	Opening Balance of loan	Principal Part	Interest Part	Annual Payment	Closing Balance
1	234,000.00	36,833.88	28,080.00	64,913.88	197,166.12
2	197,166.12	41,253.94	23,659.93	64,913.88	155,912.18
3	155,912.18	46,204.42	18,709.46	64,913.88	109,707.76
4	109,707.76	51,748.95	13,164.93	64,913.88	57,958.82
5	57,958.82	57,958.82	6,955.06	64,913.88	0.00
-	Total	234,000.00	90,569.39	324,569.39	-

c) Annual payments are made at the end of the year. So from the amortization table we can see that half of the loan is paid at the end of 3rd year. Half of loan = 234,000 / 2 = 117000

d) From the amortization table we can see that total interest paid = $90,569.39