contestada

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

Respuesta :

sqdancefan

Answer:

  5.9 years

Step-by-step explanation:

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

  [tex]V(t)=P(1+\dfrac{r}{n})^{nt}[/tex]

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

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

Otras preguntas