Find the amortization table for a $13,000 loan amortized in five annual payments if the interest rate is 8.1% per year compounded annually. (Round your answers to the nearest cent.)
End of
Period Payment Payment
Toward
Interest Payment
Toward
Principal Outstanding
Principal
0 13000
1
2
3
4
5
To find the amortization table for a $13,000 loan amortized in five annual payments with an interest rate of 8.1% per year compounded annually, we need to calculate the payment amount and the distribution of each payment towards interest and principal.
First, let's find the annual payment amount. We can use the formula for calculating the monthly payment on an installment loan to find the annual payment amount:
\[ P = \dfrac{rPV}{1 - (1 + r)^{-n}} \]
where P is the payment amount, r is the interest rate per period, PV is the present value (loan amount), and n is the total number of periods.
In this case, r = 0.081 (8.1% expressed as a decimal), PV = $13,000, and n = 5. Plugging in these values:
\[ P = \dfrac{0.081 \times 13000}{1 - (1 + 0.081)^{-5}} \]
Calculating this, we find that P ≈ $3,478.77.
Now, let's create the amortization table.
End of
Period Payment Payment
Toward
Interest Payment
Toward
Principal Outstanding
Principal
0 $3,478.77 - - $13,000
1 $3,478.77 $1,053.00 $2,425.77 $10,574.23
2 $3,478.77 $853.80 $2,624.97 $7,949.26
3 $3,478.77 $642.55 $2,836.22 $5,113.04
4 $3,478.77 $417.14 $3,061.63 $2,051.41
5 $3,478.77 $175.43 $3,303.34 $0.00
In each period, the payment amount is $3,478.77. The payment toward interest is calculated by multiplying the outstanding principal balance at the beginning of each period by the interest rate (8.1%), and the payment toward principal is the difference between the total payment amount and the interest payment.
The outstanding principal balance at the end of each period is the previous outstanding principal balance minus the payment toward principal.
Please note that the above numbers have been rounded to the nearest cent.
To find the amortization table for a loan, we need to calculate the payment toward interest, payment toward principal, and the outstanding principal for each period.
First, let's calculate the annual payment amount using the formula for calculating the payment on a fixed-term loan:
Payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
where:
P = Principal amount of the loan = $13,000
r = Annual interest rate = 8.1% = 0.081
n = Number of periods = 5 (since it's a 5-year loan)
Substituting the given values into the formula:
Payment = 13000 * (0.081 * (1 + 0.081)^5) / ((1 + 0.081)^5 - 1)
Now, calculate each period's payment toward interest, payment toward principal, and the outstanding principal:
Period 1:
To calculate the payment toward interest:
Interest Payment = Outstanding Principal * Interest Rate
Outstanding Principal = Principal Amount
Payment toward Interest = Principal Amount * Interest Rate = 13000 * 0.081
Payment toward Principal = Payment - Payment toward Interest
Outstanding Principal = Outstanding Principal - Payment toward Principal
Repeat the above calculations for each period (2 to 5), using the updated outstanding principal from the previous period until you reach the end of the loan term.
Here's the complete amortization table:
End of
Period Payment Payment
Toward
Interest Payment
Toward
Principal Outstanding
Principal
0 13000
1
2
3
4
5
To fill in the table, you will need to perform the calculations outlined above for each period.