I must use the equation A=Pe^rt. I am given the initial investment P=$7500 And I am given the amount of time that it will double (21years) I must find the annual %rate and the amount of money after ten years. Please use detailed step by step process so I can understand! (thanks so much!)

Question

anonymous · Answer

$$2=e^{21r}$$solve for $r$

anonymous · Answer

in log form it is $$\ln(2)=21r$$so $$r=\frac{\ln(2)}{21}$$

anonymous · Answer

then a calculator http://www.wolframalpha.com/input/?i=log%282%29%2F21

anonymous · Answer

and then i guess turn your answer in to a percent by moving the decimal over two places left

hlares · Answer

Alright, so, we have P=7,500 and T=21 for the first part and we need to find R=annual percentage rate for the second part. Again, we will be using the natural logarithm to find and the fact that lnx=c and e^c=x.
15,000=(7,500)*e^(21r)
2=e^(21r)
ln(2)=21r
ln(2)/21=r
r=0.03300...
So, we will round the annual percentage rate to two significant decimal places: R=0.033

Now that we have R, we can find how much money we will have after ten years:
A=(7,500)*e^(10*0.033)
A=(7,500)*e^(0.33)
A=10,432.261
Thus, we will have $10,432.26 after ten years.

hlares · Answer

I should add with the annual percentage rate: for the calculations, I left it as a decimal point. For the actual percent you will write down, multiply R=0.033 by 100 for R=3.3%.