how much would $500 invested at 4% interest compounded continuously be worth after 7 years? Round your answer to the nearest cent. Do not include units in the answer.
To find the final amount of money after 7 years with continuous compounding, we use the formula:
A = P * e^(rt)
Where:
A = Final amount
P = Principal amount (initial investment)
e = Euler's number (approximately 2.71828)
r = Interest rate
t = Time in years
Given:
P = $500
r = 4% = 0.04
t = 7
Substituting the values into the formula:
A = 500 * e^(0.04 * 7)
Using a calculator:
A ≈ 500 * e^(0.28)
A ≈ 500 * 1.32313
A ≈ 661.565
Rounding this to the nearest cent, the final amount would be $661.57.
To find the value of an investment that is continuously compounded, you can use the formula:
A = P * e^(rt)
Where:
A = the final amount
P = the principal (initial investment)
e = Euler's number 2.71828...
r = annual interest rate (as a decimal)
t = time in years
In this case, the principal (P) is $500, the interest rate (r) is 4% (or 0.04 as a decimal), and the time (t) is 7 years.
Plugging in the values into the formula:
A = 500 * e^(0.04 * 7)
To calculate this, we need to use the value of Euler's number (e). You can either use a calculator with a built-in "e^x" function or approximate it by using the rounded value of 2.71828.
A ≈ 500 * 2.71828^(0.04 * 7)
Calculating this expression will give you the final amount (A). Round your answer to the nearest cent, which means rounding to two decimal places without including any units.
Please note that without knowing the exact value of Euler's number (e), the result will be an approximation, and hence, the answer will also be an approximation.
To calculate the result accurately, you may use a scientific calculator or any online calculator that supports exponentiation and rounding to decimal places.