## Saving for the Future

What initial amount should a tutor put into an investment with a 7% effective annual rate to have a future worth of $15,000 in 5 years?

##
__
__**Hint**

**Hint**

The question is asking for the present value/worth,
$$P$$
, given the future worth,
$$F$$
.

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__**Hint 2**

**Hint 2**

Single Payment Present Worth:

$$$P=F(1+i)^{-n}$$$

where
$$i$$
is the interest rate per interest period, and
$$n$$
is the number of compounding periods.

The question is asking for the present value/worth (initial principal balance),
$$P$$
, given the future worth,
$$F$$
. Single Payment Present Worth:

$$$P=F(1+i)^{-n}$$$

where
$$i$$
is the interest rate per interest period, and
$$n$$
is the number of compounding periods.

$$$P=\$15,000(1+0.07)^{-5}=\$10,694.79$$$

The tutor should put in $10,694.79 as an initial investment.

$10,694.79