What interest rate would a $5,000 investment have to earn in order to double in 8 years assuming it is compounding monthly?
How would you set this up and work out?
You want to double your money in eight years. So if it were compounded annually, you might want to solve for i as follows:
(1+i)^8 = 2
However, you've got monthly compounding here. So you'll want to solve for i/12 instead of i, to reflect the monthly compounding. The other thing you'll need to do is change the exponent (8) to reflect monthly compounding as well. Since we're compounding 12 times per year for 8 years, we'll want to use an exponent of 8*12 = 96, resulting in the following equation:
(1+i/12)^96 = 2
Then, solve the above for i (using natural logs is probably the best way) and you should be good to go.
- Steve