In: Finance
33. Construct an amortization schedule for a $1,000, 8% annual rate loan with 3 equal payments. The first payment will be made at the end of the1st year. Find the required annual payments: $338.0
34. Based on the information from Question 33, what’s the ending balance of the amortized loan at the end of the third year: $0
35. Based on the information from Question 33 and 34, calculate the total amount of interests you should pay for the amortized loan in three years.
A. $128.8
B. $145.4
C. $150.0
D. $164.1
33. Required annual payments is $388.03 and not $338.00 ( I will give the working at the end of this solution).
34. $0 is correct.
35. Total payment towards loan = $388.03 * 3 = $1,164.10
When you subtract the loan amount from total payment we get the total interest.
Total interest = $1,164.10 - $1,000 = $164.10
So the answer is D. $164.1
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.
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Now come back to 33.
I am using present value of annuity formula to find the yearly payment:
Where,
PVA = Present value of annuity
A = Annuity
i = Interest rate in decimal form
n = Number of years
Substituting the values, we get:
.
Amortization table:
Loan Amortization table | ||||
Year | Payment | Interest portion | Principal portion | Loan balance |
0 | - | - | - | $1,000.00 |
1 | $388.03 | $80.00 | $308.03 | $691.97 |
2 | $388.03 | $55.36 | $332.68 | $359.29 |
3 | $388.03 | $28.74 | $359.29 | $0.00 |
Total | 1,164.10 | 164.10 | 1,000.00 | - |
Excel formulas and functions used in above table: