Questions: You deposit 5000 in an account earning 2% interest compounded monthly. How much will you have in the account in 15 years?

Transcript text: You deposit $\$ 5000$ in an account earning $2 \%$ interest compounded monthly. How much will you have in the account in 15 years? \$ $\square$

Solution

Solution Steps

Step 1: Identify the Given Values

We are given the following values:

Principal amount ($P$): \$5000
Annual interest rate ($r$): 2% or 0.02
Number of compounding periods per year ($n$): 12 (monthly)
Number of years ($t$): 15

Step 2: Apply the Compound Interest Formula

The compound interest formula is: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Substituting the given values into the formula: \[ A = 5000 \left(1 + \frac{0.02}{12}\right)^{12 \times 15} \]

Step 3: Calculate the Future Value

First, calculate the monthly interest rate: \[ \frac{0.02}{12} = 0.0016667 \] Next, calculate the exponent: \[ 12 \times 15 = 180 \] Now, compute the future value: \[ A = 5000 \left(1 + 0.0016667\right)^{180} \] \[ A \approx 5000 \left(1.0016667\right)^{180} \] \[ A \approx 5000 \times 1.3495 \] \[ A \approx 6747.61 \]