Question

If 8000 dollars is invested in a bank account at an interest rate of 10 per cent per year, find the amount in the bank after 15 years if interests is compounded continuously

Answer 1

The formula for continuously compounded interest is given by the formula A = P * e^(rt), where A is the amount in the bank after t years, P is the principal amount (initial investment), r is the annual interest rate, and t is the time in years.

In this case, P = $8000, r = 10% = 0.10, and t = 15 years.

Substituting these values into the formula, we get:
A = 8000 * e^(0.10 * 15)

Using a calculator, we find that e^(0.10 * 15) ≈ 4.0467.

Therefore, the amount in the bank after 15 years would be:
A = 8000 * 4.0467 ≈ $32,373.60

Therefore, the amount in the bank after 15 years with continuous compounding is approximately $32,373.60.