Question

You want to buy an Audi A8 7 years from now. You have priced these cars and found that they currently sell for $83,800. You believe that the price will increase by 10% per year for the next 7 years. You can presently invest to earn 10% annual interest, compounded annually. How much will you need to invest every year (hint: PMT) to be able to afford to buy the car in 7 years?

Answer 1

Answer:

We to invest $ 17,213 per year to buy the car in  seven years from now

Explanation:

First, we solve for the future value of the car:

$Principal \: (1+ r)^{time} = Amount$

Principal 83,800.00

time 7.00

rate 0.10000

$83800 \: (1+ 0.1)^{7} = Amount$

Amount 163,302.49

Then, for the PTM to achieve tham amount in 7 years:

$FV \div \frac{(1+r)^{time} -1}{rate} = C$

FV 163,302

time 7

rate 0.1

$163302.49298 \div \frac{(1+0.1)^{7} -1 }{0.1} = C$

C  $ 17,212.981