find the amount of money accumulated if you invested $10,000 at 5.4% interest for 8 years compounded continuously.
the total will be
10000*e^(8*.054) = 15,403.35
To find the amount of money accumulated when investing $10,000 at 5.4% interest compounded continuously for 8 years, we can use the formula for continuous compound interest:
A = Pe^rt
Where:
- A is the amount accumulated
- P is the principal amount (initial investment)
- e is Euler's number, approximately 2.71828
- r is the interest rate (in decimal form)
- t is the time period (in years)
In this case,
P = $10,000
r = 5.4% = 0.054 (converted to decimal)
t = 8 years
Using these values in the formula, we have:
A = 10,000 * e^(0.054 * 8)
Calculating the exponent, we get:
A = 10,000 * e^(0.432)
Using a calculator, we can evaluate e^(0.432) to be approximately 1.54053. Multiplying this by $10,000, we get:
A = 10,000 * 1.54053
A ≈ $15,405.30
Therefore, the amount of money accumulated after 8 years, with continuous compounding at a 5.4% interest rate, would be approximately $15,405.30.