Finance. A person wishes to have $\$ 18,600$ cash for a new car 7 years from now. How much should be placed in an account now, if the account pays $4.3 \%$ annual interest rate, compounded weekly?
(Round to the nearest dollar.)
Answer
Final Answer: The amount that should be placed in the account now is \(\boxed{13767}\) dollars.
Step 1 ：We are given that the future value (FV) is $18,600, the annual interest rate (r) is 4.3% or 0.043, the interest is compounded weekly so n is 52, and the time (t) is 7 years.
Step 2 ：We can use the formula for the present value (PV) which is \(PV = \frac{FV}{(1 + \frac{r}{n})^{nt}}\)
Step 3 ：Substituting the given values into the formula, we get \(PV = \frac{18600}{(1 + \frac{0.043}{52})^{52*7}}\)
Step 4 ：Calculating the above expression, we get PV = 13767.158872039194
Step 5 ：Rounding to the nearest dollar, we get PV = 13767
Step 6 ：Final Answer: The amount that should be placed in the account now is \(\boxed{13767}\) dollars.
