Answer:
It would take 6 years for the value of the account to reach $5,920
Step-by-step explanation:
Principal Amount = $4900
Interest rate r = 3% = 0.03
Compounded monthly = n=12
Time t =?
Future Value = $5920
We can find time using formula: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Putting values and solving:
[tex]A=P(1+\frac{r}{n})^{nt}\\5920=4900(1+\frac{0.03}{12})^{12t} \\5920=4900(1+0.0025)^{12t}\\5920=4900(1.0025)^{12t}\\\frac{5920}{4900}= (1.0025)^{12t}\\1.21=(1.0025)^{12t}[/tex]
Applying exponent rule; [tex]a=b^c\\c\:ln(b)=ln(a)[/tex]
[tex]12t\:ln(1.0025)=ln(1.21)\\12t\:(0.00249)=0.19062\\t=\frac{0.19062}{12*0.00249}\\t=6.3\approx6[/tex]
So, It would take 6 years for the value of the account to reach $5,920
