Find the payment necessary to amortize the loan using the amortization table. Round to the nearest cent.
-$32,000, 8% compounded semiannually, 20 semiannual payments

Question

Find the payment necessary to amortize the loan using the amortization table. Round to the nearest cent. 
-$32,000, 8% compounded semiannually, 20 semiannual payments

Quizplus · Accepted Answer

Using the given values, we can set up the amortization table as follows:

| Payment | Interest Paid | Principal Paid | Loan Balance |
|---------|--------------|----------------|--------------|
| 1       | $2,560.00       | $1,292.80         | $30,707.20       |
| 2       | $2,446.18       | $1,406.62         | $29,300.58       |
| 3       | $2,329.65       | $1,523.14         | $27,777.44       |
| 4       | $2,210.22       | $1,642.57         | $26,134.87       |
| 5       | $2,087.63       | $1,765.16         | $24,369.71       |
| 6       | $1,961.65       | $1,891.14         | $22,478.57       |
| 7       | $1,832.01       | $2,020.78         | $20,457.80       |
| 8       | $1,698.45       | $2,154.35         | $18,303.45       |
| 9       | $1,560.67       | $2,292.13         | $16,011.32       |
| 10      | $1,418.38       | $2,434.42         | $13,576.90       |
| 11      | $1,271.30       | $2,581.50         | $10,995.39       |
| 12      | $1,119.09       | $2,733.71         | $8,261.68        |
| 13      | $961.42         | $2,891.39         | $5,370.29        |
| 14      | $797.94         | $3,054.87         | $2,315.42        |
| 15      | $628.29         | $3,224.52         | $0.00            |

The payment necessary to amortize the loan is the same as the principal paid in each payment, which is $1,292.80 for the first payment. However, since the payments decrease as the loan balance decreases, we need to find the total amount of all 20 payments to get the total amount paid on the loan. Adding up all the principal paid results in:

$1,292.80 * 20 = $25,856.00

Therefore, the answer is B) $2,354.56, which is the payment amount per payment required to amortize the loan with a total payment of $47,091.20. Using the formula for the periodic payment on an amortizing loan,
P = (PV*r)/(1 - (1+r)^(-n)), where PV is the present value of the loan, r is the periodic interest rate, and n is the total number of periods, we can plug in the given values and calculate the payment to be $2,354.56.

Find the Payment Necessary to Amortize the Loan Using the Amortization