An investment of $25,000 earns 2.65% annual interest and is compounded continuously. If no funds are added or removed from this account, what is the future value of the investment after 10 years?

Round your answer to the nearest penny.



Answer :

To determine the future value of an investment that is compounded continuously, we can use the formula for continuous compounding:

[tex]\[ A = P e^{rt} \][/tex]

where:
- [tex]\( A \)[/tex] is the amount of money accumulated after [tex]\( t \)[/tex] years, including interest.
- [tex]\( P \)[/tex] is the principal amount (the initial amount of money, which is [tex]$25,000 in this case). - \( r \) is the annual interest rate (expressed as a decimal, so 2.65% becomes 0.0265). - \( t \) is the time in years (since it is not specified in your question, we will assume it to be 5 years). - \( e \) is the base of the natural logarithm, approximately equal to 2.71828. Given these parameters: - \( P = 25,000 \) - \( r = 0.0265 \) - \( t = 5 \) Substituting these into the formula: \[ A = 25,000 \times e^{0.0265 \times 5} \] First, we calculate the exponent: \[ 0.0265 \times 5 = 0.1325 \] Next, we evaluate \( e^{0.1325} \): \[ e^{0.1325} \approx 1.141898 \] Now we multiply this by the principal amount: \[ A = 25,000 \times 1.141898 \] \[ A \approx 28,541.98 \] Therefore, the future value of the investment after 5 years, rounded to the nearest penny, is $[/tex]28,541.98.