Answer:
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
[tex]FV=PV\left(1+r\right)^t[/tex]
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
[tex]PV=FV\left(1+r\right)^{-t}[/tex]
The Annual Percentage Rate (APR) is 6.8% compounded weekly, so the value of r is (assuming 52 weeks per year)
[tex]\displaystyle r=\frac{6.8}{100\times 52}=0.00131[/tex]
And the time is computed in weeks
t=4*52=208
The present value of the investment Trevor needs to save now is
[tex]PV=12,000\left(1+0.00131\right)^{-208}[/tex]
[tex]\boxed{PV=\$9,143.88}[/tex]
Trevor will need to invest $9,143.88 into the account to have $12,000 after 4 years
