Question

you deposit $500 annually into an account with a 6% annual interest rate. if you plan to make these deposits for the next 5 years, how much will you have in the account in 5 years?
a $2,818.54
b $2,800.66
c $2,106.18
d $2,215.45

Explanation:

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

Step 1: Identify the values

• $P = 500$ (annual deposit)
• $r = 0.06$ (annual interest rate)
• $n = 5$ (number of years)

Step 2: Plug into the formula

First, calculate $(1 + r)^n$: $(1 + 0.06)^5 \approx 1.3382255776$

Then, calculate $(1 + r)^n - 1$: $1.3382255776 - 1 = 0.3382255776$

Next, calculate $\frac{(1 + r)^n - 1}{r}$: $\frac{0.3382255776}{0.06} \approx 5.63709296$

Finally, calculate $FVA$: $FVA = 500 \times 5.63709296 \approx 2818.55$ (which is close to option A)

Answer:

A. $2,818.54$