An investment is made at an annual rate of 9.71% compounded monthly, determine the number of months required for your investment to double.

Pt = Po(1+r)^n = 2Po.

r=(9.71% / 12mo) / 100% = 0.00809167=
Monthly % rate expressed as a decimal.

Po(1+r)^n = 2Po,
Divide both sides by Po:
(1+r)^n = 2Po / Po,
(1+r)^n = 2,
Take Log of both sides:
n*Log(1+r) = Log2,
n = Log2 / Log(1+r),
n = Log2 / Log(1.008091666667) = 86
Compounding Periods.

86comp. * 1mo./comp. = 86 months.

86 months

To determine the number of months required for an investment to double, we need to use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A = the final amount (double the initial investment)
P = the principal (initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years

In this case, we want to find the number of months required, so we need to convert the annual interest rate and the time to months. The annual interest rate is given as 9.71%, so we convert it to a decimal by dividing it by 100:

r = 9.71% รท 100 = 0.0971

Also, since the interest is compounded monthly, n = 12 (months in a year).

We want to find the time required to double the investment, so A = 2P.

Substituting all the values into the compound interest formula, we have:

2P = P(1 + 0.0971/12)^(12t)

Next, we can cancel out the P's:

2 = (1 + 0.0971/12)^(12t)

Now, we need to solve for t. To make the equation easier to solve, let's take the natural logarithm (ln) of both sides:

ln(2) = ln[(1 + 0.0971/12)^(12t)]

Using the property of logarithms, we can bring the exponent down:

ln(2) = 12t * ln(1 + 0.0971/12)

Finally, we can solve for t by dividing both sides by 12 * ln(1 + 0.0971/12):

t = ln(2) / (12 * ln(1 + 0.0971/12))

Using a calculator, we can evaluate this expression to find the value of t.

Note: Make sure you are using a calculator or software capable of evaluating natural logarithms (ln).