Question

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

Compound interest formula: V(T)=P(1+r/n)^nt

t = years since initial deposit
n = number of times compounded per year
r = annual interest rate (as a decimal)
P = initial (principal) investment
V(t) = value of investment after t years

p.S: Please explain, I have a couple problems like this so having an example to go off of would be nice. :)
x Thanks

Answer 1

The really answer is A which is 5.9 years

Answer 2

If you want the money to double:
V ( t ) = 2 P
n = 4 ( because it is compounded quarterly )
r = 0.12 ( annual interest rate )
2 P = P * ( 1 + 0.12/4 ) ^(4t) / : P ( we divide both side of equation by P )
2 = ( 1 + 0.03 )^(4t)
2 = ( 1.03 )^(4t)
and because (1.03)^24 ≈ 2 ( using calculator )
4 t = 24
t = 24 : 4
t = 6
Answer: It will take 6 years.