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 ​$244,000 for Custom Autos if Custom Autos will make an annual payment to LCI at an interest rate of 11% 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?

(round to the nearest cent)

Answer 1

A.

outstanding amount (P) =   244000
Interest rate annual is 11% or   0.11

TOTAL years (n)= 5

Equal annual payments for loan formula = P* i *((1+i)^n)/((1+i)^n-1)      
244000*0.11*((1+0.11)^5)/(((1+0.11)^5)-1)      
=$66,019.16      

So annual Payment is $66019.16

B.

So, interest and principal payment is calculated in following amortization table.                  
   Loan amortization table              
Year   Beginning balance   Payment   Interest    Principal payment   Ending balance
                  
           (Beg. Bal.*0.11)   (Payment - interest)   (Beg. Balance - Loan red.)
1   244000.00   66019.16   26840.00   39179.16   204820.84
2   204820.84   66019.16   22530.29   43488.86   161331.98
3   161331.98   66019.16   17746.52   48272.64   113059.34
4   113059.34   66019.16   12436.53   53582.63   59476.72
5   59476.72   66019.16   6542.44   59476.72   0.00
                  
                  
Total 330095.78   86095.78   244000.00  

C. Half of Balance = 244000/2= $12200

As we see in schedule, in year 3 closing balance is $113059.34. so Balance be half paid in year 3.

D. Total ínterest paid over loan is $86095.78

Formula = (Total Payment - Amount Outstanding)

=(5*66019.16)-244000

=$86095.78