WILL GIVE MEDAL: Sally invests $4000 in a savings account which compounds interest monthly. After 10 years, she has a balance of $5,451.52. What is the annual interest rate of the account, rounded to the nearest 0.01%?

Question

anonymous · Answer

I have it set up just need help solving it. :o

anonymous · Answer

n = 10*c= 12*10 = 120

I = rate/c = ?

P = 4000

A = 5451.20

anonymous · Answer

I meant 5451.52

anonymous · Answer

This is what I have it set up as:

5451.52= 4000(1+ r/12)^ 12*10

anonymous · Answer

good.

anonymous · Answer

I just dunno how to solve for the r I've been lost :o

anonymous · Answer

$$1.36288 = (1+\frac{r}{12})^{120}\ \sqrt[120]{1.36288} = (1+ \frac{r}{12})$$

anonymous · Answer

$$1.00258 = ( 1 + \frac{r}{12})\0.0025833 = \frac{r}{12}$$

anonymous · Answer

Awesome! So after the last step do I multiply by 12 to get the r?

anonymous · Answer

yes

anonymous · Answer

I got .0309996 did yo happen to get the same answer?

anonymous · Answer

X 100 = ?

anonymous · Answer

3.10% is..that an intuitive answer? would that be a reasonable interest rate for this financial interaction?

anonymous · Answer

Yes, it would! Thank you so much for your help! I appreciate it! :)