The worth after 10 years if it were invested at 4% interest compounded continuously is $ 895.094
<h3><u>Solution:</u></h3>
Given that $ 600 invested at 4 % interest compounded continously for 10 years
To find: total amount after 10 years
<em><u>The compound interest formula for compounded continously is given as:</u></em>
![A = p e^{rt}](https://tex.z-dn.net/?f=A%20%3D%20p%20e%5E%7Brt%7D)
Where "p" is the principal
"r" is the rate of interest
"t" is the number of years
Here in this problem, p = 600
![r = 4 \% = \frac{4}{100} = 0.04](https://tex.z-dn.net/?f=r%20%3D%204%20%5C%25%20%3D%20%5Cfrac%7B4%7D%7B100%7D%20%3D%200.04)
t = 10 years
Substituting the values in formula we get,
![A = 600 e^{0.04 \times 10}\\\\A = 600 e^{0.4}\\\\A = 600 \times 1.49182469764\\\\A = 895.094](https://tex.z-dn.net/?f=A%20%3D%20600%20e%5E%7B0.04%20%5Ctimes%2010%7D%5C%5C%5C%5CA%20%3D%20600%20e%5E%7B0.4%7D%5C%5C%5C%5CA%20%3D%20600%20%5Ctimes%201.49182469764%5C%5C%5C%5CA%20%3D%20895.094)
Thus the worth after 10 years is $ 895.094