## Housing Down Payment

Consider a new grad engineer wants to start saving for a housing down payment. With current real estate prices, she'll need $100,000 within 5 years. How much will she need to invest annually if she plans on holding a typical index fund that historically returns 10% annually? Ignore inflation.

##
__
__**Hint**

**Hint**

The problem is asking for the uniform amount per interest period,
$$A$$
, given the future worth,
$$F$$
.

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__**Hint 2**

**Hint 2**

Uniform Series Sinking Fund:

$$$A=F\cdot \frac{i}{(1+i)^{n}-1}$$$

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

The problem is asking for the uniform amount per interest period,
$$A$$
, given the future worth,
$$F$$
. Uniform Series Sinking Fund:

$$$A=F\cdot \frac{i}{(1+i)^{n}-1}$$$

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

$$$A=\$100,000\cdot \frac{0.1}{(1+0.1)^{5}-1}=\frac{\$10,000}{(1.1)^5-1}=\$16,380$$$

$16,380