# Math Help - Macroeconomics Math Problem Help, Please?

1. ## Macroeconomics Math Problem Help, Please?

Consider a hypothetical economy that grows at a rate of 4% per year. Approximately how many years will it take for this economy to double in size?
Note: the size of an economy is its real GDP.
Hint: to solve this problem, you first want to set up an equation that links the future size of the economy to its current size and the growth rate.

Honestly I have no idea where to start. If anyone has any clue as to solve this I would greatly appreciate some help!

2. ## Re: Macroeconomics Math Problem Help, Please?

Originally Posted by michellederz
Consider a hypothetical economy that grows at a rate of 4% per year. Approximately how many years will it take for this economy to double in size?
Note: the size of an economy is its real GDP.
Hint: to solve this problem, you first want to set up an equation that links the future size of the economy to its current size and the growth rate.

Honestly I have no idea where to start. If anyone has any clue as to solve this I would greatly appreciate some help!
think of the economy as a bank account with some interest rate.

It's future value FV (FV) is given, in terms of the interest rate (R), time (T), and present value (PV) as

$$FV=PV(1+R)^T$$

In this problem you are looking for the time T it takes for FV/PV=2, i.e. the economy has doubled.

$$2=(1+0.04)^T$$

$$\log(2)=T\log(1.04)$$

$$T=\frac{\log(2)}{\log(1.04)}$$

$$T \approx 17.67\text{yrs}$$

3. ## Re: Macroeconomics Math Problem Help, Please?

Originally Posted by romsek
think of the economy as a bank account with some interest rate.

It's future value FV (FV) is given, in terms of the interest rate (R), time (T), and present value (PV) as

$$FV=PV(1+R)^T$$

In this problem you are looking for the time T it takes for FV/PV=2, i.e. the economy has doubled.

$$2=(1+0.04)^T$$

$$\log(2)=T\log(1.04)$$

$$T=\frac{\log(2)}{\log(1.04)}$$

$$T \approx 17.67\text{yrs}$$
Ahhh! That makes so much more sense thinking of it in those terms. Thank you so much.