Question

I have a question about recognizing FV and PV. I searched the solution of Q1 and Q2 and finds out that, in Q1, $225,000 is an FV, while in Q2, $68,000 is a PV. However, I think they should both be FV or both be PV since they are both the price for a new purchase.

Q1: You're trying to save to buy a new $225,000 Ferrari. You have 45,000 today that can be invested in your bank. The bank pays 4.8 percent annual interest on its accounts. How long will it be before you have enough to buy the new car?

Q2: You want to buy a new sports car from Muscle Motors for $68,000. The contract is in the form of a 60-month annuity due at an APR of 6.4 percent. What will your monthly payment be?

Answer 1

Question 1:

FV = $225,000

PV = $45,000

r = 4.8% or 0.048

FV = PV (1+r)^t

In this question, FV = $225,000. It is because $225,000 is the amount required to purchase the Ferrari car at future point of time. Hence, the future value of the car is considered as FV.

Solving for t,

t = ln (FV/PV) / ln (1+r)

= ln ($225,000 / $45,000) / ln (1.048)

= 34.3 years

Note:

ln refers to natural logarithm, which you can find in a scientific calculator.

Question 2:

In this we need to use PV Annuity due equation, to determine monthly payment.

Monthly Rate (r) = APR / Corresponding Period

                         = 0.064 / 12

                         = 0.0053

In this question $68,500 is considered as Present Value of Annuity due, because it is the current value of series of cash flow payments to be made in regular intervals, either beginning or end of the month.

PVA_due = C x PV

PVA_due = C x [ 1 – {1 / [1 + (r)⁶⁰ } ] / r

$68,500 = C x [ 1 – {1/ 1.0053⁶⁰ } ] / 0.0053

$68,500 = C x [ 1- 0.7281] / 0.0053

$68,500 x 0.0053 = C x 0.2719

$363.05 = C x 0.2719

C = $363.05 / 0.2719

   = $1335.23

Hence, the monthly payment would be $1335.23

Note:

• C refers to monthly payment