1. ## Interest Rate

Find the interest rate needed for an investment of $7,000 to grow to$10,500 in 6 yr if interest is compounded monthly. (Round your answer to the nearest hundredth of a percentage point.)

2. You are supposed to show some effort. Do you know the formula for the total amount after n month? If yes, what is your difficulty?

3. a = p (1+ r/m) ^mt
??

4. Yes, so $\displaystyle 10500=7000(1+r/12)^{12\cdot6}$, i.e., $\displaystyle (1+r/12)^{72}=1.5$. By raising both sides to 1/72, you can find r.

5. idk how to take the log and find r...

6. do u want me to take 72th root of both sides?

7. if i take the 72th root of both sides then r = 0 ...?

8. if i take the 72th root of both sides then r = 0 ...?
No, if $\displaystyle (1+r/12)^{72}=1.5$, then $\displaystyle 1+r/12=(1.5)^{1/72}=\sqrt[72]{1.5}\approx1.00565$.

9. ok i got it..
thanks the answer came out right..
r = 6.80 rounded

10. But the other problem i am not able to figure out and i have 1 more try left its the last one..

11. Use logarithms to solve the equation for t.

12. $\displaystyle \displaystyle\frac{A}{1+Be^{t/2}}=C$ iff
$\displaystyle A=C(1+Be^{t/2})$ and $\displaystyle 1+Be^{t/2}\ne0$.

$\displaystyle A=C(1+Be^{t/2})$ iff
$\displaystyle A=C+BCe^{t/2}$ iff
$\displaystyle A-C=BCe^{t/2}$ iff
$\displaystyle (A-C)/(BC)=e^{t/2}$ or $\displaystyle (A-C=0 and B=0)$.

$\displaystyle (A-C)/B=e^{t/2}$ iff
$\displaystyle \ln((A-C)/(BC))=t/2$.

13. SO T = 2ln((A-C)/BC))

right?

14. yessssssss its right!!!

thankkkk kyouuuuu soo muchhhh i appreciate your help very muchhhhh

15. You are welcome.