An investment of $2000 doubles every 12 years. How much is the investment worth after 36 years? 60 years?

Question

How much is the investment worth after 36 years? 60 years? Model the value of the invest with an exponential function 

Answer 1

First you need to determine the interest rate.  I am assuming that the interest is compounded annually,

 

2000(1 + i)^ 12 = 4000

(1+i)^12 = 2

log(1+i)^12 = log 2

12*log(1+i) = log 2

log(1+i) =(log 2)/12 = 0.025086

1+i = 10^0.025086 = 1.05946

i = 0.05946 or 5.946%

 

To model the value of the investment:  2000(1.05946)^n  where n = years

 

2000(1.05946)^36 = $16,000

2000(1.05946)^60 = $64,000

 

Al Berglund

 

 

 

 

 

 

Answer 2

Initially, $2000

After 12 years, $4000

After 24 years, $8000 (another twelve years, so doubled the 4K)

After 36 years, $16,000

After 48 years, $32,000

After 60 years, $64,000