Question

saving a total of 1000 dollars per year for 20 years, at 5% interest compounded continuously, will give a final savings amount of dollars. evaluate this integral to compute the final savings. round your answer to the nearest dollar.

Answer 1

To find the final savings amount after 20 years of saving $1000 per year at 5% interest compounded continuously, use the formula A = P * e^(rt). Plugging in the values, the final savings amount is $2653.

Step-by-step explanation:

To find the final savings amount after 20 years of saving $1000 per year at 5% interest compounded continuously, we can use the formula:

A = P * e^(rt)

Where:
A is the final amount
P is the principal amount (initial savings)
e is the base of the natural logarithm, approximately 2.71828
r is the interest rate
t is the time in years

Plugging in the values, we get:
A = 1000 * e^(0.05 * 20)

Using a calculator, we find that the value of e^(0.05 * 20) is approximately 2.6533:

A = 1000 * 2.6533 = $2653.30

Rounding to the nearest dollar, the final savings amount is $2653.