Question

future value. kyle has $1,500 in cash received for high - school graduation gifts from various relatives. he wants to invest it in a certificate of deposit (cd) so that he will have a down payment on a car when he graduates from college in five years. his bank will pay 3.7% per year, compounded annually, for the five - year cd. how much will kyle have in five years to put down on his car? in five years, the amount kyle will have to put down on his car is $ (ignore the effect of income taxes and round your answer to the nearest cent.) (use your financial calculator or you may use the financial tables in appendix c in computing your answer.)

Explanation:

Step1: Identify the compound - interest formula

The formula for continuous compounding is $A = Pe^{rt}$, where $P$ is the principal amount, $r$ is the annual interest rate, $t$ is the number of years, and $A$ is the future value. Here, $P=\$1500$, $r = 0.037$, and $t = 5$.

Step2: Substitute the values into the formula

$A=1500\times e^{0.037\times5}$.
First, calculate the exponent: $0.037\times5 = 0.185$.
Then, find the value of $e^{0.185}$. Using a calculator, $e^{0.185}\approx1.2032$.
Now, $A = 1500\times1.2032=\$1804.8$.

Answer:

$1804.80$