Question - Continuous Compounding Calculation for Future Value
mathothercompound interest calculationfuture value formulacontinuous compounding calculationinterest earned calculation
Solution:
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, ande is the base of the natural logarithm (approximately equal to 2.71828).Based on the information provided in the image:P = $5500r = 3.6% or 0.036 (as a decimal)t = 8 yearsWe 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 = 0.288Now, 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 ≈ 7337.22So 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 - PInterest earned ≈ 7337.22 - 5500 ≈ 1837.22Therefore, the amount of interest earned is approximately $1837.22. Remember to verify these calculations using a calculator for precision.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com