Question

chapter 6 quiz score: 0/25 answered: 0/7 question 1 you deposit $2000 each year into an account earning 6% interest compounded annually. how much will you have in the account in 30 years? $ submit question

Explanation:

Step1: Identify the formula

We use the future - value of an ordinary annuity formula $FVA = A\times\frac{(1 + r)^{n}-1}{r}$, where $A$ is the annual payment, $r$ is the interest rate per period, and $n$ is the number of periods.

Step2: Define the values

Here, $A=\$2000$, $r = 0.06$ (since 6%=0.06), and $n = 30$.

Step3: Substitute the values into the formula

$FVA=2000\times\frac{(1 + 0.06)^{30}-1}{0.06}$.
First, calculate $(1 + 0.06)^{30}$:
$(1 + 0.06)^{30}=1.06^{30}\approx5.743491173$.
Then, $(1 + 0.06)^{30}-1\approx5.743491173 - 1=4.743491173$.
$\frac{(1 + 0.06)^{30}-1}{0.06}=\frac{4.743491173}{0.06}\approx79.05818622$.
$FVA = 2000\times79.05818622=\$158116.37$.

Answer:

$158116.37$