A student deposits a $500 in a bank account that pays 4.8% interest compounded continuously. What will the account be worth after 18 months?
I set this problem up as A(t) = 500e^(0.048*1.5). But the answer I get is incorrect. The correct answer is $1027.22.
Well, to do this, you're correct! You set up the equation as follows for compound interest:
`A(t) = Pe^(rt)`
Where A is your final amount, P is your principle, e is the base of the natural log, r is your annual rate, and t is time in years.
So, our variables are as follows:
`P = 500`
`r = 0.048`
`t = 18/12 = 1.5`
So, your final equation is:
`A(1.5) = 500e^(0.048*1.5) =537.33`
Now, this answer most certainly doesn't agree with the "correct" answer. So, let's set up the equation and solve backwards to figure out how the "correct" answer was found:
`1027.22 = 500e^(0.048t)`
This must be the form they had, so let's solve for t:
Start by dividing by 500:
`2.05444 = e^(0.048t)`
Now, take the natural log of both sides:
`ln(2.05444) = 0.048t`
And finally, divide by 0.048:
`ln(2.05444)/0.048 = 15 = t`
There's the problem! Whoever calculated the correct answer used either 15 for t, or they could have used 0.48 instead of 0.048 for r. Either way, that textbook typo is what caused the problem.
So, if you got $537.33, you're right! If not, now you know how to get it.
SIDE NOTE Before I went ahead and said the correct answer was wrong, I input the values given in the problem into multiple interest calculators online..they all gave the same answer. Also, the "correct" answer makes no sense intuitively, because at 5% interest, there is absolutely no way to double your money in 1.5 years! If so, I'd love to see the math behind it!