suppose you invest $1100 at an annual interest rate of 4.3% compounded continuously. How much will you have in the account after 15 years?
balance = investment * e^rt
= 1100 e^(.043 * 15)
= 1100 * 1.9059
= $ 2096.59
To find the amount of money you will have in the account after 15 years, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the final amount
P = the principal amount (initial investment)
e = the base of natural logarithms (approximately 2.71828)
r = the annual interest rate (in decimal form)
t = the time period in years
In this case, P = $1100, r = 4.3% = 0.043, and t = 15.
Let's calculate it step by step:
Step 1: Convert the interest rate to a decimal form:
r = 4.3% = 0.043
Step 2: Substitute the values into the formula:
A = 1100 * e^(0.043 * 15)
Step 3: Calculate the exponent:
A = 1100 * e^(0.645)
Step 4: Use a calculator to evaluate e^(0.645):
A ≈ 1100 * 1.904
Step 5: Multiply the principal amount by the result:
A ≈ 2,094.38
Therefore, you will have approximately $2,094.38 in the account after 15 years.