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

Do you understand the formula and the variables for it?

Answer 2

Kind of..

Answer 3

If we want some sum of money (call it P dollars) to double, how much money do we want to end up with?

Answer 4

Double the amount?

Answer 5

yeah you start with P and it doubles to ???

Answer 6

the 12%? ..

Answer 7

that's the interest rate

Answer 8

Let's say you start off with P = 100 dollars

That doubles to $200

so what they want is the time it takes to go from $100 to $200

Answer 9

to do that, you solve for t in


\[\Large V(t) = P\left(1+\frac{r}{n}\right)^{n*t}\]
\[\Large 200 = 100\left(1+\frac{0.12}{4}\right)^{4*t}\]

Answer 10

But I'm confused because it doesn't give me sum to plug in, how am I supposed to know what to double?

Answer 11

you can start off with any amount, it doesn't matter

Answer 12

the doubling time does NOT change based on the starting amount

the doubling time depends on the interest rate and the compounding frequency

Answer 13

Thank you for trying to help, I think i'll just ask my teacher tomorrow though.

Answer 14

alright, that works