Questions: You deposit 2000 in an account earning 4% interest compounded monthly. How much will you have in the account in 5 years?

You deposit 2000 in an account earning 4% interest compounded monthly. How much will you have in the account in 5 years?

Solution

Solution Steps

Step 1: Convert the Annual Interest Rate to Decimal

To use the annual interest rate in calculations, we convert it from a percentage to a decimal form by dividing by 100. Thus, the decimal form of the annual interest rate \(r\) is \(r = 4 / 100 = 0.04\).

Step 2: Apply the Compound Interest Formula

The future value \(FV\) can be calculated using the formula \(FV = P(1 + \frac{r}{n})^{nt}\), where \(P\) is the principal amount, \(r\) is the annual interest rate in decimal form, \(n\) is the number of times the interest is compounded per year, and \(t\) is the time in years. Substituting the given values, we get \(FV = 2000(1 + \frac{0.04}{12})^{12*5}\).

Step 3: Calculate the Future Value

After performing the calculations, the future value of the investment or deposit is approximately \(FV = 2441.99\).