Question

Ali invests $4,078 in a retirement account with a fixed annual interest rate of 7% compounded

continuously. What will the account balance be after 14 years? (round your answer to the nearest
dollar, and do NOT put a $ in your answer.

Answer 1

The account balance will be $10,866 after 14 years

Explanation:

Compound continuous interest can be calculated using the formula:

`A=Pe^(rt)`

• A = the future value of the investment, including interest

• P = the principal investment amount (the initial amount)

• r = the interest rate

• t = the time the money is invested for

Let us use this rule to solve the question

∵ Ali invests $4,078 in a retirement account

∴ P = 4,078

∵ The account with a fixed annual interest rate of 7% compounded

continuously

∴ r = 7% =
`(7)/(100)` = 0.07

∵ The time is 14 years

∴ t = 14

Substitute these values in the rule above to find A

∵
`A=4,078(e)^(0.07(14))`

→ Use the calculator to find the value of A

∴ A = 10,865.65255

→ Round it to the nearest dollar

∴ A = $10,866

∴ The account balance will be $10,866 after 14 years