To complete the table for an account in which interest is compounded continuously, we need to calculate the amount after 10 years and after 25 years.
To calculate the amount after a certain time using continuous compounding, we can use the formula:
A = P * e^(rt)
Where:
A is the final amount
P is the initial investment
e is Euler's number (approximately 2.71828)
r is the annual interest rate (in decimal form)
t is the time in years
Let's calculate the amount after 10 years:
P = $50,000
r = 12% = 0.12 (as a decimal)
t = 10 years
Plugging these values into the formula, we have:
A = $50,000 * e^(0.12 * 10)
Using a calculator, we find that e^(0.12 * 10) is approximately 3.32012. Multiplying this by $50,000 gives us:
A = $50,000 * 3.32012 = $166,006
Therefore, the amount after 10 years is $166,006.
Now, let's calculate the amount after 25 years:
P = $50,000
r = 12% = 0.12 (as a decimal)
t = 25 years
A = $50,000 * e^(0.12 * 25)
Again, using a calculator, we find that e^(0.12 * 25) is approximately 7.20049. Multiplying this by $50,000 gives us:
A = $50,000 * 7.20049 = $360,025
Therefore, the amount after 25 years is $360,025.
To summarize:
- Amount after 10 years: $166,006
- Amount after 25 years: $360,025
