Jerome will be buying a used car for $9 comma 0009,000 in 22 years. How much money should he ask his parents for now so that, if he invests it at 99% compounded continuouslycontinuously, he will have enough to buy the car?
Nine million dollars for a used car? In 22 years???
Ridiculous!!
To find out how much money Jerome should ask his parents for now, we need to calculate the future value of the investment at a continuous compounding rate of 99% over 22 years.
The formula to calculate the future value (FV) of an investment with continuous compounding is:
FV = P * e^(rt)
Where:
FV = Future Value
P = Principal amount (amount Jerome asks his parents for)
e = Euler's number (approximately 2.71828)
r = Annual interest rate (in decimal form)
t = Time period in years
In this case, the principal amount (P) is unknown, the interest rate (r) is 99% or 0.99, and the time period (t) is 22 years.
Let's plug in the values and solve for P:
FV = P * e^(0.99 * 22)
To isolate P, we can divide both sides by e^(0.99 * 22):
FV / e^(0.99 * 22) = P
Now we can calculate the value of P:
P = $9,000 * e^(0.99 * 22)
Using a calculator, compute the value of e^(0.99 * 22) and multiply it by $9,000 to find the principal amount Jerome should ask his parents for.