On August 1,a $30,000,6%,3-year installment note payable is issued by a company.The note requires equal payments of principal plus accrued interest be paid each year on July 31.The present value of an annuity factor for 3 years at 6% is 2.6730.The present value of a single sum factor for 3 years at 6% is 0.8396.The payment each July 31 will be:
A)$10,000.00.
B)$11,223.34.
C)$80,190,00.
D)$10,400.00.
E)$1,223.34.

Question

Quizplus · Accepted Answer

To find the payment, we need to use the present value of an annuity formula which requires us to know the present value of the note.

PV of note = $30,000 x 0.8396 = $25,188

Now, we can use the present value of an annuity formula:

PMT = PV / PV of annuity factor
PMT = $25,188 / 2.6730
PMT = $9,423.84

However, the question asks for equal payments of principal plus accrued interest, so we need to add the interest component to the payment.

Interest in Year 1 = $30,000 x 6% = $1,800
Principal = PMT - Interest in Year 1 = $9,423.84 - $1,800 = $7,623.84

Therefore, the payment each July 31 will be:

PMT = Principal + Interest in Year 1 = $7,623.84 + $1,800 = $9,423.84

This payment will be made for 3 years, so the total payments over the life of the note will be:

Total Payments = PMT x # of years = $9,423.84 x 3 = $28,271.52

This is greater than the face value of the note, so we know we've done our calculations correctly.

On August 1,a $30,000,6%,3-Year Installment Note Payable Is Issued by a Company.The