Final answer:
To calculate the value of an investment with continuous compound interest, use the formula A = P*e^(r*t), where A is the final amount, P is the principal investment, r is the annual interest rate, t is the time in years, and e is the base of the natural logarithm. For each scenario, the calculated values are as follows: A) $8,677.72, B) $872.51, C) $4,993.25.
Step-by-step explanation:
A) Calculation:
To find the value of the investment after 14 years with continuous compound interest, we can use the formula:
A = P*e^(r*t)
Where:
A is the final amount
P is the principal investment
r is the annual interest rate
t is the time in years
e is the base of the natural logarithm, approximately 2.71828
Given:
Principal investment P = $4,300
Annual interest rate r = 5.4% or 0.054
Time t = 14 years
Calculating:
A = $4,300 * e^(0.054 * 14)
Using a calculator, we find that the value of the investment after 14 years is approximately $8,677.72.
B) Calculation:
Using the same formula:
A = P*e^(r*t)
Given:
P = $550
r = 3.3% or 0.033
t = 14 years
Calculating:
A = $550 * e^(0.033 * 14)
Calculating with a calculator, the value of the investment after 14 years is approximately $872.51.
C) Calculation:
Using the formula:
A = P*e^(r*t)
Given:
P = $2,200
r = 4.6% or 0.046
t = 14 years
Calculating:
A = $2,200 * e^(0.046 * 14)
Using a calculator, the value of the investment after 14 years is approximately $4,993.25.