Math help please!

Question

How long (in years and months) will it take for an investment to double at 5% compounded monthly?

Answer 1

A(t) = A₀(1 + r/n)^nt

• A(t) = amount of money you have at time t = 2A₀
• r = annual interest rate as a decimal = 5% = 0.05
• n = number of compoundings per year = monthly = 12
• t = years

 

A(t) = A₀(1 + r/n)^nt

2A₀ = A₀(1 + 0.05/12)^12t

2 = (1.00417)^12t

log₂(2) = log₂(1.00417^12t)

1 = 12t·log2(1.00417)        [log properties: log_a(a) = 1, log(a^b) = b·log(a)]

1/[12·log₂(1.00417)] = t

 

Use your calculator to get the answer in years.  Convert to years and months.