The amount of money in an account can be determined by the formula A re where is the initial investment, r is the annual interest rate, and tis the number of ye
Mathematics
jeffrey629
Question
The amount of money in an account can be determined by the formula A re where is the
initial investment, r is the annual interest rate, and tis the number of years the money was
invested. What is the value of a $5000 investment after 18 years, if it was invested at 4% interest
compounded continuously?
2 Answer

1. User Answers Eduard22sly
Answer: $10272.17
Stepbystep explanation: Please see attachment for explanation

2. User Answers freckledspots
Answer:
[tex]\$10272.17[/tex]
Stepbystep explanation:
Since it is compounded continuously, we will use:
[tex]A=A_0 \cdot e^{k t}[/tex]
[tex]A_0[/tex] is the amount invested.
[tex]k[/tex] is the rate.
[tex]t[/tex] is the number of years you let the money sit.
[tex]A[/tex] is the future amount after the [tex]t[/tex] years that has been accumulated.
(Note:
I'm going to write [tex]r=4%[/tex] as a decimal. [tex]r=\frac{4}{100}=0.04[/tex].)
[tex]A=5000 \cdot e^{0.04 \cdot 18}[/tex]
[tex]A=5000 \cdot e^{0.72}[/tex]
[tex]A=5000 \cdot 2.0544332[/tex] (approximated)
[tex]A=10272.16605[/tex] (approximated)
To the nearest cent this is [tex]\$10272.17[/tex].