Respuesta :
Answer:
After [tex]26.91\ years[/tex] the principle amount value will reach to [tex]26400\ dollars[/tex].
Step-by-step explanation:
Given that,
Principle Amount [tex](P)= 7100\ dollars[/tex]
Rate of Interest [tex](R)=[/tex] [tex]5[/tex]%
Total Amount [tex](A)= 26400\ dollars[/tex]
If Principle Amount [tex](P)[/tex] [tex]=P\ dollars[/tex], Time [tex]=t\ years[/tex], Rate of Interest [tex]=R[/tex]% [tex]pa[/tex]
when interest is compounded annually:
Total Amount after [tex]t\ years[/tex] [tex]= P(1+\frac{R}{100}) ^{t}[/tex]
Now,
[tex]A= P(1+\frac{R}{100}) ^{t}[/tex]
⇒ [tex]26400=7100(1+\frac{5}{100}) ^{t}[/tex]
⇒ [tex]3.7183=(1+0.05)^{t}[/tex]
⇒ [tex]3.7183=(1.05)^{t}[/tex]
taking log both sides, we get
[tex]ln(3.7183)=ln {(1.05)^{t}}[/tex]
⇒ [tex]1.31327=t\times ln(1.05)[/tex]
⇒ [tex]1.31327=t\times 0.04879[/tex]
⇒ [tex]t=26.91[/tex]
Therefore,
After [tex]26.91\ years[/tex] the principle amount value will reach to [tex]26400\ dollars[/tex].
