Question

Paul invests $8,000 in an account that pays an interest rate of 5% compounded continually. Using the formula A = Pe^rt, calculate the balance after 7 years.

a) $10,498.06
b) $11,352.54
c) $14,500.96
d) $9,554.00

Answer 1

The balance of Paul's investment after 7 years with a 5% interest rate compounded continually is calculated using the formula A = Pe^rt. Plugging in the values, the balance is found to be $11,352.54, which is option (b).

Step-by-step explanation:

To calculate the balance of Paul's investment after 7 years with a 5% interest rate compounded continually, we use the formula A = Pert, where:

• P is the principal amount (initial investment),
• r is the annual interest rate (in decimal form),
• t is the time in years,
• e is the base of the natural logarithm (approximately 2.71828).

Plugging the values into the formula, we get:

A = $8,000 * e0.05*7

A = $8,000 * e0.35

A = $8,000 * 1.4190675 (using a calculator for e0.35)

A = $11,352.54

Therefore, the balance of the account after 7 years is $11,352.54, which corresponds to option b).