Cindy will require $15,000 in 2 years to return to college to get an MBA degree. How much money should she ask her parents for now so that, if she invests it at 12% compounded continuously, she will have enough for school?

Question

Cindy will require $15,000 in 2 years to return to college to get an MBA degree. How much money should she ask her parents for now so that, if she invests it at 12% compounded continuously, she will have enough for school?

Answer 1

To find out how much money Cindy should ask her parents for now, we need to calculate the future value of her investment. The formula for continuous compound interest is given by:

A = P * e^(rt)

Where:
A = Final amount (future value)
P = Principal amount (initial investment)
e = Euler's number (approximately 2.71828)
r = Annual interest rate (expressed as a decimal)
t = Time (in years)

In this case, Cindy wants to have $15,000 in 2 years, so we need to solve for P. Let's plug in the given values into the formula:

$15,000 = P * e^(0.12 * 2)

Now, let's solve for P. Since the exponential function involves e, we'll use the natural logarithm function (ln) to isolate P:

ln($15,000) = ln(P * e^(0.12 * 2))

Using the properties of logarithms, we can simplify the equation:

ln($15,000) = ln(P) + 0.12 * 2

ln($15,000) ≈ ln(P) + 0.24

Now, let's isolate ln(P) by subtracting 0.24 from both sides:

ln(P) ≈ ln($15,000) - 0.24

Using a calculator, we can find the natural logarithm of $15,000:

ln($15,000) ≈ 9.6158

Now, substitute this value back into the equation:

ln(P) ≈ 9.6158 - 0.24

ln(P) ≈ 9.3758

Finally, to find the value of P (the amount Cindy should ask her parents for now), we need to take the inverse of the natural logarithm using the exponential function (e^x):

P ≈ e^(9.3758)

Using a calculator, we can find the value of e^(9.3758):

P ≈ $11,160.03

Therefore, Cindy should ask her parents for approximately $11,160.03 to have enough funds for her MBA degree when invested at 12% compounded continuously.

Answer 2

The continuous interest formula is

A=Pe^rt
A=future amount, 15000
P=principal (unknown)
e=euler's constant, 2.71828..
r=rate of interest, 0.12 for 12%
t=time in years (for annual rate of interest), 2 years

So
15000=P*e^0.12*2
P=15000/(e^0.24)

Can you take it from here?

Do a check by the reverse calculation, to see if
P*e^0.24 gives 15000.