Question

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

Answer 1

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.

Answer 2

86 months