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Find the interest earned on $5,600 deposited for 5 years at annual interest rate compounded continuously.

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The interest earned on $5,600 deposited for 5 years at an annual interest rate compounded continuously is approximately $1177.60.

To find the interest earned on $5,600 deposited for 5 years at an annual interest rate compounded continuously, we can use the formula:

A = P * e^(rt)

where:

A is the final amount after 5 years

P is the principal amount ($5,600)

e is Euler's number (approximately 2.7183)

r is the annual interest rate (as a decimal, not a percentage)

t is the time in years (5 years)

1: Convert the interest rate to a decimal

The interest rate is given as an annual rate, but we need it as a decimal for the formula. So, divide the annual rate by 100:

r = 0.05

2: Calculate the final amount (A)

A = 5600 * e^(0.05 * 5)

A ≈ 6777.60

3: Calculate the interest earned

The interest earned is the difference between the final amount (A) and the principal amount (P):

Interest earned = A - P

Interest earned ≈ 6777.60 - 5600

Interest earned ≈ $1177.60

Therefore, the interest earned on $5,600 deposited for 5 years at an annual interest rate compounded continuously is approximately $1177.60.

User Cyrielle
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