Emma receives $7750 and invests it in an account that earns 4% interest
compounded continuously. What is the total amount of her investment after 5 years?
P = Po*e^rt.
P = Principal amt. after 5 yrs.
Po = $7750 = Initial investment.
rt = (4%/100%)*5 = 0.20.
Solve for P.
Answer: $9465.87.
To find the total amount of Emma's investment after 5 years, we'll use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the total amount after time t
P = the initial principal (initial investment)
e = the mathematical constant approximately equal to 2.71828
r = the annual interest rate (as a decimal)
t = the number of years the money is invested for
In this case, Emma's initial principal (P) is $7750, the annual interest rate (r) is 4% (0.04 as a decimal), and the time (t) is 5 years.
Substituting the values into the formula:
A = $7750 * e^(0.04 * 5)
Now, we can calculate the total amount by raising e to the power of (0.04 * 5) and then multiplying it by $7750:
A ≈ $7750 * e^0.2
Using a calculator or a computer program to calculate e^0.2, we find:
A ≈ $7750 * 1.221403
Calculating the product:
A ≈ $9456.76
Therefore, the total amount of Emma's investment after 5 years is approximately $9456.76.
To find the total amount of Emma's investment after 5 years with continuous compounding interest, we can use the formula:
A = P * e^(rt)
Where:
A = the total amount of the investment after time t
P = the principal amount (initial investment)
e = the mathematical constant approximated as 2.71828
r = the interest rate (in decimal form)
t = the time period in years
In this case, Emma's principal amount (P) is $7750, the interest rate (r) is 4% (or 0.04 in decimal form), and the time period (t) is 5 years.
Plugging in the values into the formula:
A = 7750 * e^(0.04 * 5)
To calculate the value of e^(0.04 * 5), we can use a calculator or the exponential function on most scientific calculators. The result is approximately 1.221402758.
Now, let's calculate the final amount:
A = 7750 * 1.221402758
A = 9470.79
Therefore, the total amount of Emma's investment after 5 years with continuous compounding interest is approximately $9470.79.