You have a 1000 to invest in an account with a rate of 8% compounded semi annually. How long will it take you to double your money?

Question

How can you solve this question with these formulas 

A=P(1+r/n)nt

N=N0(1/2) t/h

Answer 1

All you need is the first equation.

 

Amount = Investment(1+rate/number of times it is compounded)^(number of times it is compounded*time)

Since the final amount we are looking for is double the initial investment of 1000, A=2000 and P=1000. Since the rate is 8%, r=0.08. Since it is compounded semi annually (or twice a year), n=2. So you end up with:

 

2000=1000(1+0.08/2)^2t -> 2=(1+0.08/2)^2t -> 2=(1.04)^2t

 

Turn the equation into a logarithm.

 

log_1.042=2t -> t=(1/2)(log_1.042) -> t=(1/2)(log2/log1.04) -> t=(1/2)(17.7) -> t=8.85

 

It would take approximately 8.85 years.

Answer 2

Hello, thank you for taking the time to post your question!

The formula that you want to use to solve this one is

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

A = final amount = 1000 x 2 = 2000

P = principal = 1000

r = interest rate = 8% = 0.08

n = compounds per year = 2

t = number of years = what we are solving for

that means that the underlying equation here for this scenario is

2000 = 1000(1 + 0.08/2)^(2*t)

From there then you can solve for the value of “t” using logarithms! When I do that I end up getting t = 8.84, meaning that it will take about 8.84 years to double your money in this particular scenario.

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)