Respuesta :
Answer:
After [tex]23.7\ years[/tex] the amount [tex]7500\ dollars[/tex] will reach to [tex]25200\ dollars[/tex].
Step-by-step explanation:
Given that,
Principle Amount [tex](P)[/tex] [tex]=7500\ dollars[/tex]
Rate of Interest [tex](R)[/tex] [tex]=5.25[/tex] %
Total Amount [tex](A)[/tex] [tex]= 25200\ dollars[/tex]
Now,
If Principle [tex]=P[/tex] [tex]dollars[/tex], Time [tex]= t[/tex] years, Rate [tex]=R[/tex]% [tex]pa[/tex]
then, Amount after [tex]t[/tex] years [tex]=A=P(1+\frac{R}{100}) ^{t}[/tex]
⇒ [tex]A=P(1+\frac{R}{100}) ^{2}[/tex]
⇒ [tex]25200=7500(1+\frac{5.25}{100} )^{t}[/tex]
⇒ [tex]3.36=(1+0.0525)^{t}[/tex]
⇒ [tex]3.36=(1.0525)^{t}[/tex]
taking log both sides, we get
⇒ [tex]ln(3.36)=ln(1.0525^{t})[/tex]
⇒ [tex]1.21194=t\times ln(1.0525)[/tex]
⇒ [tex]1.21194=t\times 0.05117[/tex]
⇒ [tex]t=23.7[/tex]
Therefore,
After [tex]23.7\ years[/tex] the amount [tex]7500\ dollars[/tex] will reach to [tex]25200\ dollars[/tex].
So, the time taken for reaching 7500 to 25200 is 2.9 years.
To understand the calculations, check below
Compound Intrest:
The formula for finding the amount with the help of compound interest is,
[tex]A=P(1+r)^t[/tex]
Given that,
[tex]Amount=25200\\r=5.25\%=0.525\\Principal=7500[/tex]
Now, substituting the given values into the above formula we get,
[tex]A=P(1+r)^t\\25200=7500(1+0.525)^t\\3.36=(1.525)^t\\[/tex]
Taking log both sides we get,
[tex]ln(3.36)=tln(1.525)\\1.212=t\times 0.422\\t=2.9[/tex]
Learn more about the topic Compound Intrest:
https://brainly.com/question/24924853
