I am having a hard time understanding when an annuity is considered present valu

Question

I am having a hard time understanding when an annuity is considered present value or future value. I can understand when talking about single amounts but when annuities are involved I get confused. My teacher says this problem is a present value, how do I tell that from the way it is worded?
"Don James purchased a new automobile for $20,000. He made a cash down payment of $5,000 and agreed to pay the remaining balance in 30 monthly installments beginning one month from the date of purchase. Financing is available at a 24% annual rate. Calculate the amount of the required monthly payment."

Explanation / Answer

The best way to answer these questions is to put the information on a timeline. For the one you have provided, $20,000 for a new auto and $5,000 down payment are both happening in the present. You are financing the difference of $15,000 with a loan payable in 30 monthly installments (i.e. annuity). You have a present amount and constant payments at the end of the month, so this is the case of a present value of an ordinary annuity (PVA). PVA = Payment x PVA Factor (annual i%, n periods) For monthly payments, divide annual i% by 12 to get a monthly interest rate since monthly payments are involved. 15,000 = Payments x PVA Factor (2%, 30) Payments = 15,000 / PVA Factor (2%, 30) Look up the PVA table for the appropriate factor and solve for P. Hope this helps.

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