Question

An initial investment of $50,692 earns 6% interest compounded monthly. How many months will it take for the investment to double?

Show work

Answer 1

A formula for calculating compound interest is

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

Where,

A = final amount
P = principal amount (initial investment)
r = annual nominal interest rate (as a decimal)

(it should not be in percentage)

n = number of times the interest is compounded per year
t = number of years

This is the starting point.

Answer 2

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

Sorry, missed a t

Answer 3

so how do u solve this

Answer 4

?

Answer 5

So, you know some information already.

Double the initial investment is 101384,

101384 = 50692 (1 + 0.06/12)^nt

Answer 6

Do a little calculating and rearranging, you get:

101384/50692 = (1.005)^nt
2 = (1.005)^nt

Should be looking a little easier by now.

Answer 7

The last step is to find out how many months (nt) it takes. You can do this as follows:

ln(2) = ln((1.005)^nt)
ln(2) = ln(1.005) * nt
ln(2)/ln(1.005) = nt

You may need a calculator for this, but is should work out to around 139 months.