compound interest rate formula question?

Question

what interest rate would we need compounded monthly for an investment of $500 to grow to $1000 in 6 years? The formula is A=P(1+ r/n)^n*t

I know how to plug it all in to solve for r, but cant figure out how to isolate to solve the problem. If you can please show work or even explain to me how you get the answer, i would appreciate it very very much. thanks in advance.

Answer 1

You do have all the components, just solve for r:

A = 1000
P = 500
n = 12 (compounded monthly)
t = 6

Thus,

1000 = 500(1+[r/12])^[12*6]

2 = (1+[r/12])^72

take the 72nd root of 2 and you get:

1+[r/12] = 1.0096

Solving for 'r', you get r = 0.116 = 11.6%

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Hope this helps

Answer 2

1000 = 500 (1 + r/12) ^ 12(6)

1000 = 500 (1 + r/12) ^ 72

Divide both sides by 500

2 = (1 + r/12) ^ 72

Raise both sides to 1 / 72 power

2 ^ (1/72) = 1+ r/12

Subtract 1 from both sides

2 ^ (1/72) -1 = r/12

Multiply both sides by 12 and you get r

r=12 ( 2^ (1/72) -1 ) =0.116 approx

Answer 3

Note that for large n e^r = (1+ r/n)^n.
So 1000 = 500 e^(6r) or r = Log[2]/6 = 0.115