Question

What annual rate of interest is required to triple an investment in 11 years ?

Answer 1

Do you know the formula for compounded interest?

Answer 2

@leibystrauss umm I have written down 3p=p (1+r/1) ^11

Answer 3

Have you been using \[A = \left( 1+\frac{ r }{ n } \right)^n\]

Answer 4

Yes @leibystrauss

Answer 5

Ok. Does the equation you wrote earlier make sense?

Answer 6

@leibystrauss I don't know because I'm following my notes I took in class

Answer 7

This formula is not for compounded interest that is not continuous; in the formula that you wrote interest would be added once a year.

Answer 8

But it says what annual rate @leibystrauss

Answer 9

I think the formula needs to be re-written

\[A = \left( 1 + \frac{ r }{ n } \right)^{nt}\]

P = principal or initial investment

If the money triples it is 3 p

t = time in years

r = rate

the n can be though of as periods

r/1 means there is one period a year, the rate is applied once a year

So essentially r/1 = r

Since there is one period in the year nt = 1(t) = t

t = 11 because it's 11 years

Now you need to solve for r

Does it make sense now?

Answer 10

Yes, would I divide by three or get rid of the exponent first? @leibystrauss

Answer 11

r/1 = r
\[3p = p \left( 1 + r \right)^{11}\]
what can you divide both sides by?

Answer 12

P? @leibystrauss

Answer 13

Correct, so re-write it.

Answer 14

@leibystrauss 3=(1+r) ^11

Answer 15

Ok. So how can you get rid of the 11th power?

Answer 16

If
\[8 = x^3\]
How would you solve for x?

Answer 17

Don't you cube root?

Answer 18

You are technically correct. But I was thinking of something else.

If

\[16 = x^4\]

How would you solve for x using a calculator?

Answer 19

I'm not sure

Answer 20

To remove the power of 4, you can raise both sides to the inverse of 4. Meaning raise both sides to 1/4

\[16^{\frac{ 1 }{ 4 }} = (x^{4})^{\frac{ 1 }{ 4 }}\]

\[=> 16^{\frac{ 1 }{ 4 }} = x^1\]

Answer 21

Ohh I see

Answer 22

So what is the next step in your problem?

Answer 23

What that mean I'd do 3^1/11=(1+r) ?

Answer 24

Correct. And the final step?

Answer 25

Subtract 1 from both sides ?

Answer 26

Yes. You technically have your answer now. If you need the rate in % form then multiply your final answer by 100.

What did you get as your final answer?

Answer 27

Um first I got a negative number so that seemed wrong, so I tried it different and then I got 0.1=r

Answer 28

What do you have after the 1?

Recall 6.4% = 0.064 so you can't round 0.064 to 0.1

Answer 29

I did 3^(1/11) && got 1.10 then I subtracted 1 && got 0.1

Answer 30

You should have another digit after the 0

Answer 31

1.105

Answer 32

Correct, so if you do multiply it by 100 rate = 10.5%

Answer 33

Thank you so much, I appreciate it (: