Please, I am begging for help with this compound interest question!?

Question

An investment doubles in 5 years. What is the annual interest rate if the interest is compounded monthly?

Answer 1

Suppose the amount of your investment is X.

Then if this doubles in 5 years (5*12 = 60 months) with compound interest, you would have, according to the formula:

2X = X (1+k)^60

Now you can cancel the "X" both sides of the equation:

2 = (1+k)^60

then

2^(1/60) = 1 + k
1.012 = 1 + k

k = 0.012

So the interest rate is 1,2% compounded monthly.

The annual interest rate (capitalized monthly) would then be

0.012 * 12 = 0.144 = 14,4 %

Answer 2

Use the natural log function.

If an amount doubles due to compound interest in any given amount of time, then we can represent it this way:

2 = (1 + i)^n, where i is the interest rate paid per period and n is the number of compounding periods. In this case, we know n = 60.

Since the numbers above are equal, so are their natural logs.

2 = (1 + i)^60
ln 2 = 60 ln (1 + i)
(ln 2) / 60 = ln (1 + i)
0.6931 / 60 ≈ ln (1 + i)
0.0116 ≈ ln (1 + i)

Now find the natural antilog of 0.0116. It's approximately 1.0117.

So (1 + i) = 1.0117 and i = 1.0117 - 1.0000 = 0.0117.

The last number above is the nominal interest rate per month expressed as a decimal. To convert it to a percentage, we just multiply it by 100 %. To find the interest rate per year, we multiply the second number by 12.

0.0117 x 100 % x 12 = 14.04 %

The account is earning approximately 14 % per annum.

To verify this is correct, simply divide 14 by 1200. Then add 1 to it and raise that sum to the 60th power. That result should be very close to 2.

Answer 3

About .1394 per year.

(1+i/12)^60 = 2 (solve for i)
60 log (1 + i/12) = log 2
10 ^ {(1/60)(log2)} = 1 + i/12
and so on.

Answer 4

2 = (1+r)^60
Solve for r.

Answer 5

I already answered this question.