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
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.