Future Value of $4,000 Investment at 2.3% Interest

You deposit $4,000 today in an account that pays 2.3% interest per year with annual compounding. How much will you have in the account 10 years from today? Round your answer to the nearest penny.

To calculate the future value of a deposit with annual compounding interest, you can use the formula:

[ FV = P(1 + r)^n ]

where:

• ( FV ) is the future value of the investment/loan, including interest,
• ( P ) is the principal investment amount (the initial deposit or loan amount),
• ( r ) is the annual interest rate (decimal),
• ( n ) is the number of years the money is invested or borrowed.

In this case:

• ( P = 4000 )
• ( r = 0.023 ) (2.3% as a decimal)
• ( n = 10 )

Now, plug in the values:

[ FV = 4000(1 + 0.023)^{10} ]

Calculating ( (1 + 0.023)^{10} ):

[ 1 + 0.023 = 1.023 ]

Now raise it to the power of 10:

[ 1.023^{10} \approx 1.243 ]

Now multiply by the principal:

[ FV \approx 4000 \times 1.243 ]

Calculating that gives:

[ FV \approx 4972 ]

So, rounding to the nearest penny, the amount in the account 10 years from today will be approximately:

[ \boxed{4972.00} ]