You invest $4500 into an account that earns 6.5% interest compounded monthly.

Question

 How long will it take for the account to double in its value?

Answer 1

The formula for compound interest is:

 

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

 

P = the amount invested

r = the rate of interest

n = the number of times during the year it is calculated

t = the number of years 

 

9000 = 4500 ( 1 + 0.0054 )^12t

2 = ( 1.0054 )^12t

log 2 = 12t log 1.0054

0.3010 = 12t ( 0.0023 )

130.86 = 12t

10.90 = t

 

The amount shall double just short of 11 years.

 

 

Answer 2

first, we don't need how much you invested to figure out when it doubles. We just need the interest rate. Let x be the number of months until the investment has doubled.

 

since it's compounded monthly, we divide interest by 12

 

.065/12 = .00542

 

(1.00542)^12x = 2

 

ln 1..00542^12x = ln 2

 

12x( ln 1.00542) = ln 2

 

12x = ln 2/ln 1.00542

 

12x = 128.23

 

x = 10.7

 

 

x = 10.7 years