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 14
t = years since initial deposit
n = number of times compounded per year
r = annual interest rate (as a decimal)
P= initial principal) investment
Vo = value of investment after years
5.9 years
6.1 years
23 4 years
245, bars

Answer 1

5.9 years

Explanation:

We believe a better representation of the compound interest formula is ...

`V(t)=P(1+(r)/(n))^(nt)`

We want to find the value of t for P=1 and V(t)=2. We are told n=4, so the formula becomes ...

`2=(1+(.12)/(4))^(4t)\\\\\log{(2)}=4t\log{(1.03)}\quad\text{take logs}\\\\t=\frac{\log{2}}{4\log{1.03}}\approx\boxed{5.9\quad\text{years}}`