Present Value of an Annuity Due: Payment or receipt made at beginning of each pe

Question

Present Value of an Annuity Due:
Payment or receipt made at beginning of each period.

On January 1, 2017 ABC Company purchased land for an agreed purchase price of $42,300.
ABC gave a $10,000 cash down payment and financed the balance with a long-term note
payable. ABC signed an interest-bearing note requiring five equal annual payments of principal
and interest with the first payment due immediately at the time of purchase. The stated interest
rate was 12% & presumed reasonable. ABC’s year end is Dec. 31st.
Required:
a. Compute the amount of the payments
b. Compute interest expense for the year ended December 31, 2017.
c. What is the PV of the note at December 31, 2017?

Explanation / Answer

a. Amount of payments : $ 8,960.

Amount of financing availed of : $ 42,300 - $ 10,000 = $ 32,300.

PVA 12%, n = 5 = 3.60478

Amount of annual payments = $ 32,300 / 3.60478 = $ 8,960.32

b. Interest expense = $ 32,300 x 12 % = $ 3,876.

c. Present value of the note at December 31, 2017 = $ 32,300 - $ ( 8,960 - 3,876) = $ 27,216.

Period PV Factor at discount rate of 12 % 1 0.89286 2 0.79719 3 0.71178 4 0.63552 5 0.56743 PVA12%, n=5 3.60478

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