Question

Suzy invests $2,600 in an account that earns 2.3% annual interest, compounded continuously. What is the value of the account after 10 years? Round to the nearest dollar

Answer 1

$3,272

Explanation:

Continuous Compounding Formula

`\large \text{$ \sf A=Pe^(rt) $}`

where:

• A = Final amount
• P = Principal amount
• e = Euler's number (constant)
• r = annual interest rate (in decimal form)
• t = time (in years)

Given:

• P = $2,600
• r = 2.3% = 0.023
• t = 10 years

Substitute the given values into the formula and solve for A:

`\sf \implies A=2600e^((0.023 * 10))`

`\sf \implies A=2600e^(0.23)`

`\implies \sf A=3272.360026...`

Therefore, the value of the account after 10 years is $3,272 to the nearest dollar.