Question

A sum of money is invested at 12% compounded quarterly. About how long will it take for the amount of money to double?

Answer 1

ok so the amount invested is x
doubled is 2x

compound interst formula is

`A=P(1+ (r)/(n))^(nt)`
A=future amount
P=present amount
r=rate in decimal
n=number of times per year it is compounded
t=time in years

we know
A=2x
P=x
r=0.12
n=4
t=?


`2x=x(1+ (0.12)/(4))^(4t)`

`2x=x(1+ 0.03)^(4t)`
divide both sides by x

`2=(1+ 0.03)^(4t)`

`2=(1.03)^(4t)`

`2=(1.03)^(4t)`
take the log₁.₀₃ of both sides

`log_(1.03)(2)=log_(1.03)(1.03^(4t))`
we know that
`log_xx^n=n` so

`log_(1.03)(2)=4t`
divide both sides by 4

`(log_(1.03)(2))/(4) =t`
use calculator to aprox
5.8624430625
about 5.9 years or 5 years and 10.3 months