Question

exponential functions - basic
score: 2/5 penalty: 0.5 off
question
6700 dollars is placed in an account with an annual interest rate of 8%. how much will be in the account after 24 years, to the nearest cent?
answer

Explanation:

Step1: Identify the formula

We use the compound - interest formula (assuming it's compounded annually, the formula for compound interest is $A = P(1 + r)^t$, where $A$ is the amount of money accumulated after $t$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal form), and $t$ is the time the money is invested for in years.
Given that $P=\$6700$, $r = 8\%=0.08$, and $t = 24$ years.

Step2: Substitute the values into the formula

Substitute $P = 6700$, $r=0.08$, and $t = 24$ into the formula $A=P(1 + r)^t$.
We get $A=6700\times(1 + 0.08)^{24}$.

Step3: Calculate $(1 + 0.08)^{24}$

First, calculate $1+0.08 = 1.08$. Then, calculate $1.08^{24}$. Using a calculator, $1.08^{24}\approx6.34118071$.

Step4: Calculate the value of $A$

Multiply $6700$ by $6.34118071$: $A = 6700\times6.34118071\approx6700\times6.34118071 = 42485.910757$.

Answer:

$\$42485.91$