Continuous Compounding Calculation for Future Value
The question is asking to calculate the future value of a deposit that is compounded continuously. The formula for calculating the future value, A, when compounded continuously is given by:
A = P * e^(rt)
Where:
P is the principal amount (initial deposit),
r is the annual interest rate (expressed as a decimal),
t is the time the money is invested for in years, and
e is the base of the natural logarithm (approximately equal to 2.71828).
Based on the information provided in the image:
P = $5500
r = 3.6% or 0.036 (as a decimal)
t = 8 years
We substitute these values into the formula to calculate the future value, A:
A = 5500 * e^(0.036 * 8)
Next, we compute the exponent:
0.036 * 8 = 0.288
Now, calculate e raised to this exponent:
e^0.288 = 2.71828^0.288 ≈ 1.33404 (using a calculator)
Finally, we multiply this by the principal amount:
A ≈ 5500 * 1.33404 ≈ 7337.22
So the future value after 8 years is approximately $7337.22. If you are asked for the amount of interest earned, you would subtract the principal from the future value:
Interest earned = A - P
Interest earned ≈ 7337.22 - 5500 ≈ 1837.22
Therefore, the amount of interest earned is approximately $1837.22. Remember to verify these calculations using a calculator for precision.
