Trevor decides to start saving money for a new car. He knows he can invest money into an account which will earn 6.8% APR, compounded weekly, and would like to have saved $12,000 after 4 years. How much money will he need to invest into the account now so that he has $12,000 after 4 years.

PV=$9,143.88

Step-by-step explanation:

Compound Interest

When a principal amount (also called present value PV) is saved at some rate of interest r for some time t, the future value FV that includes the original investment plus the interests is computed as

If the investment is compounded other than annually, then r and t must be scaled to the proper time units.

If we already know the future value, then the present value is computed by solving the above equation

The Annual Percentage Rate (APR) is 6.8% compounded weekly, so the value of r is (assuming 52 weeks per year)

And the time is computed in weeks

t=4*52=208

The present value of the investment Trevor needs to save now is

Trevor will need to invest $9,143.88 into the account to have $12,000 after 4 years