Question

$10,000 is invested at 7% annual interest which is compounded continuously what is the balance after eight years with no deposits or withdrawals are made

Answer 1

$17,506.73

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 = $10,000
• r = 7% = 0.07
• t = 8 years

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

`\sf \implies A=10000e^((0.07 * 8))`

`\sf \implies A=10000e^(0.56)`

`\implies \sf A=17506.725...`

Therefore, the value of the account after 8 years is $17,506.73 to the nearest cent.