Question

You want to have $35,000 in cash to buy a car 3 years from today. you expect to earn 3.6 percent, compounded annually, on your savings. how much do you need to deposit today if this is the only money you save for this purpose? $33,726.04

Answer 1

Suppose we deposit P dollars. What we can work out is P by considering the interest that is being compounded annually.
$\text{Interest: } 3.6% = 0.036pa$
After the first year, we would have compounded our deposited amount once: $P + P(0.036) = P(1.036)^{1}$
Using the amount we have in our bank, we compounded it a second and third time: $P(1.036) \cdot (1.036) = P(1.036)^{2}; \text{Third year: } P(1.036)^{3}$

Let our third year cash be 35 000 to pay off the car.
$P(1.036)^{3} = 35000$
$P = \frac{35000}{(1.036)^{3}} = 31476.67$

Thus, P = $31, 476.67, which is the deposit that you need to make on the day.