Down Payment
Consider a young professional wants to start saving for a car down payment. They will need $20,000 within 3 years. How much money do they need to put into a high yield savings account each month if the account returns 2% monthly?
Expand Hint
The problem is asking for the uniform amount per interest period,
$$A$$
, given the future worth,
$$F$$
.
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.
$$$A=\$20,000\cdot \frac{0.02}{(1+0.02)^{36}-1}$$$
$$$=\frac{\$400}{(1.02)^{36}-1}=\frac{\$400}{1.03988}=\$384.66$$$
$384.66
Time Analysis
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