Question

E3.3 (LO 3) (Unknown Rate) HQ Ltd. purchased a used truck from Trans Auto Sales Inc. HQ paid a $4,000 down payment and signed a note that calls for 36 payments of $1,033.34 at the end of each month. The stated rate of interest in the note is 4%. As an incentive for entering into the contract, Trans has agreed to forgive the first two payments under the lease. Instructions a. What was the purchase price of the used truck excluding the incentive given

Answer 1

Answer: $35,000

Explanation:

The payments of $1,033.34 at the end of every month is a constant amount which makes it an annuity.

Present value of annuity:

= Annuity * (1 - (1 + rate) ^-no. of periods) / rate

Rate needs to be made a monthly rate:

= 4%/12

= 4/12%

= 1,033.34 * ( 1 - ( 1 + 4/12%) ⁻³⁶/ 4/12%

= $35,000

Purchase price = Down payment + Present value of annuity

= 4,000 + 35,000

= $39,000