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

Answer:

$17,506.73

Step-by-step explanation:

Continuous Compounding Formula

$\large \sf A=Pe^{rt}$

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:

$\sf \implies A=10000e^{(0.07 \times 8)}$

$\sf \implies A=10000e^{0.56}$

$\implies \sf A=17506.725...$

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