Question

I seriously need some help.
Bo Newman will invest $10,422 today in a fund that earns 8% annual interest. How many years will it take for the fund to grow to $22,500? I have the answer I just dont know how they got it. Please someone help me!!!

Answer 1

I used this formula and guess and check.
y = 10,422 (1.08)^10
y = $22,500.31

If I am not mistaken, the amount of years should be 10. Since it's exponential growth, I did 100% + 8% = 1.08 and that's the growth factor. $10,422 is the initial amount.

Answer 2

If the interest is compounded annually, the formula is\[22500=1422(1+.08)^t\]

Answer 3

The guess-and-check answer above shows an answer very close to ten years. If the interest is compounded continuously, the formula would be\[22500=10422e^{.08t}\]

Answer 4

that is the correct answer however that is not how they computed it.

Answer 5

Ok, we'll start with my equation above, and work it out.\[22500=10244(1+.08)^t \implies \frac{22500}{10244}=1.08^t\]\[\implies \ln 22500 - \ln 10422=\ln 1.08^t=tln1.08 \implies \frac{\ln 22500- \ln 10422}{\ln1.08}=t\]

Answer 6

If you slam that out with a calculator, you'll get a number satisfactorily close to ten.