Answer:
$16,976.61
Step-by-step explanation:
Okay, let's break this down into simple steps.
First, we need to find the total amount (A) after 5 years, given that $12,460 is compounded continuously at a rate of 6.2%.
We can use the formula for continuous compounding:
A = P * e^(rt)
Where:
A = the amount of money accumulated after n years, including interest
P = the principal amount (the initial amount of money)
e = the base of the natural logarithm (approximately 2.71828)
r = the annual interest rate (as a decimal)
t = the time the money is invested for in years
Here, P = $12,460, r = 6.2% = 0.062, and t = 5 years.
So, plug these values into the formula:
A = 12460 * e^(0.062 * 5)
Now, we just need to calculate e^(0.062 * 5) and then multiply it by 12,460.
Let's do that:
A ≈ 12460 * e^(0.31)
Now, we need to find e^(0.31). This is a bit tricky, but you can use a calculator or table to find it. Let's say e^(0.31) is approximately 1.3635.
So, now we can multiply:
A ≈ 12460 * 1.3635
Now, just multiply those two numbers together:
A ≈ $16,976.61
So, after 5 years, the amount would be approximately $16,976.61.
