Prepare an amortization schedule for a three-year loan of $96,000. The interest
ID: 2642653 • Letter: P
Question
Prepare an amortization schedule for a three-year loan of $96,000. The interest rate is 9 percent per year, and the loan calls for equal annual payments. How much total interest is paid over the life of the loan?(Enter rounded answers as directed, but do not use rounded numbers in intermediate calculations.Round your answers to 2 decimal places (e.g., 32.16). Leave no cells blank. You must enter '0' for the answer to grade correctly.)
Year
Beginning
Balance
Total
Payment
Interest
Payment
Principal
Payment
Ending
Balance
1
$
$
$
$
$
2
3
Prepare an amortization schedule for a three-year loan of $96,000. The interest rate is 9 percent per year, and the loan calls for equal annual payments. How much total interest is paid over the life of the loan?(Enter rounded answers as directed, but do not use rounded numbers in intermediate calculations.Round your answers to 2 decimal places (e.g., 32.16). Leave no cells blank. You must enter '0' for the answer to grade correctly.)
Explanation / Answer
Loan amortization schedule is helpful for analyzing and understanding the future liability payments and liquidity required.
Here, loan is of $ 96,000 for 3 years at 9% annual interest rate.
Now, if we need to find the interest payments each year, closing and opening balances every year, then for this we need installments amount. Since in the question it is given that the installments are equal for all the 3 years, we can find the amount of installment using the present value method.
Under present value method, sum total of present value of the installments should be equal to the loan amount as on the grant day of the loan.
Suppose today loan was granted, now find the present value of the installments at 9% to give amount of loan. We use this concept because ideally each year interest will be calculated on the beginning amount of loan at 9%.
Therefore,
Loan Amount = Present value of first installment + Present value of second installment + Present value of third installment
Since the installments are equal let us take them as = $ X
Thus, $ 96,000 = X ( Sum of present value of $ 1 at 9% for 3 years)
Sum of all Present value of $ 1 at 9% for 3 years= $ 1 / (1+9%) ^ 1 + $ 1 / (1+9%) ^ 2 + $ 1 / (1+9%) ^ 3
This will give = $ 2.531294666
Putting the above present value in below equation
$ 96,000 = X (2.531294666)
X = $ 37,925.26
With this loan amortization is given below:
Year
Beginning Balance (A)
Total Payment or Installments (B)
Interest Payment (A * 9%) ( C )
Principal Payment (B-C) (D)
Ending Balance (A-D)
1
$ 96,000.00
$ 37,925.26
$ 8,640.00
$ 29,285.26
$ 66,714.74
2
$ 66,714.74
$ 37,925.26
$ 6,004.33
$ 31,920.93
$ 34,793.81
3
$ 34,793.81
$ 37,925.26
$ 3,131.45
$ 34,793.81
$ -
Total Interest Payment
$ 17,775.78
Year
Beginning Balance (A)
Total Payment or Installments (B)
Interest Payment (A * 9%) ( C )
Principal Payment (B-C) (D)
Ending Balance (A-D)
1
$ 96,000.00
$ 37,925.26
$ 8,640.00
$ 29,285.26
$ 66,714.74
2
$ 66,714.74
$ 37,925.26
$ 6,004.33
$ 31,920.93
$ 34,793.81
3
$ 34,793.81
$ 37,925.26
$ 3,131.45
$ 34,793.81
$ -
Total Interest Payment
$ 17,775.78