Question
Find the interest earned when $22,082 is invested at 6% compounded continuously for 5 years
Answers
GPT 3.5
The formula for continuous compound interest is given by the formula:
A = P*e^(rt)
where:
A = the final amount
P = the principal amount
r = the annual interest rate (as a decimal)
t = the time in years
In this case, we are given:
P = $22,082
r = 6% = 0.06 (as a decimal)
t = 5 years
So, plugging in these values into the formula, we get:
A = 22082*e^(0.06*5)
Using a calculator, we can evaluate this expression to find:
A ≈ $29,609.60
To find the interest earned, we subtract the principal amount from the final amount:
Interest = A - P
Interest = $29,609.60 - $22,082
Interest = $7,527.60
Therefore, the interest earned when $22,082 is invested at 6% compounded continuously for 5 years is approximately $7,527.60.
A = P*e^(rt)
where:
A = the final amount
P = the principal amount
r = the annual interest rate (as a decimal)
t = the time in years
In this case, we are given:
P = $22,082
r = 6% = 0.06 (as a decimal)
t = 5 years
So, plugging in these values into the formula, we get:
A = 22082*e^(0.06*5)
Using a calculator, we can evaluate this expression to find:
A ≈ $29,609.60
To find the interest earned, we subtract the principal amount from the final amount:
Interest = A - P
Interest = $29,609.60 - $22,082
Interest = $7,527.60
Therefore, the interest earned when $22,082 is invested at 6% compounded continuously for 5 years is approximately $7,527.60.