Question

 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 $234000 for Custom Autos if Custom Autos will make an annual payment to LCI at an interest rate of 8​% 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

Outstanding bill = $234000

a). Calculating annual payment of the loan:

(1+r) Annual payment = P*r* (1+r) -1

Where, P= Loan Amount = $234000

r = Periodic Interest rate = 0.08

n= no of periods = 5

Annual Payment = 234000 * 0.08 * (1 +0.08) (1 + 0.08)5 - 1

Annual Payment = 18720 * 1.469328 (1.469328 – 1)

Annual Payments = $ 58606.82

b). Preparing the amortization schedule:-

Year	Begin Bal.	Payment	interest	Principal	End Bal
1	234000	58606.82	18720	39886.82	194113.18
2	194113.18	58606.82	15529.05	43077.77	151035.41
3	151035.41	58606.82	12082.83	46523.99	104511.42
4	104511.42	58606.82	8360.91	50245.91	54265.51
5	54265.51	58606.82	4341.24	54265.58	-0.

Table can be explained as:

- Interest = Begin Bal*8%

- Principal = Payment - Interest

- End Balance = Begin bal + interest - Payment

c). Loan Amount = $234000

Balance at the end of 3rd year = $104511.42

So, balance will be half paid at the end of 3rd year.

d). The total interest expense on the loan over the 5​years = (Annual Payment*no of payment) - Loan Amount

= ($58606.82*5)-$234000

= $ 59034.1

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