Please Help!

How much money, invested at an interest rate of r% per year compounded continuously, will amount to A dollars after t years?
A = 15,500, r = 5.4, t = 5

15500 = Pe^(.054*5)

P = 11,832.40

To calculate the amount of money needed to reach a target investment value after a certain number of years with continuous compounding, we can use the formula for compound interest:

A = P * e^(r * t)

Where:
A = Target amount
P = Principal amount (initial investment)
e = Euler's number (approximately 2.71828)
r = Interest rate (in decimal form)
t = Time (number of years)

In this case, we are given:
A = $15,500
r = 5.4% = 0.054 (convert to decimal form)
t = 5 years

To find P, the amount of money needed, we can rearrange the formula:

P = A / (e^(r * t))

Now we can substitute the given values and calculate:

P = 15,500 / (e^(0.054 * 5))

To evaluate e^(0.054 * 5), we can multiply the exponent and then use a calculator or a software that supports exponentiation functions:

P = 15,500 / (e^0.27)

P ≈ 15,500 / 1.31071

P ≈ 11,820.77

Therefore, approximately $11,820.77 needs to be invested at an interest rate of 5.4% per year compounded continuously to reach $15,500 after 5 years.