Question

7100 dollars is placed in an account with an annual interest rate of 5%. To the nearest tenth of a year, how long will it take for the account value to reach 26400 dollars ?

Answer 1

Answer:

After $26.91\ years$ the principle amount value will reach to $26400\ dollars$.

Step-by-step explanation:

Given that,

                 Principle Amount $(P)= 7100\ dollars$

                 Rate of Interest $(R)=$ $5$%

                 Total Amount $(A)= 26400\ dollars$

If Principle Amount $(P)$ $=P\ dollars$, Time $=t\ years$, Rate of Interest $=R$% $pa$

when interest is compounded annually:

Total Amount after $t\ years$ $= P(1+\frac{R}{100}) ^{t}$

Now,

         $A= P(1+\frac{R}{100}) ^{t}$

     ⇒ $26400=7100(1+\frac{5}{100}) ^{t}$

     ⇒ $3.7183=(1+0.05)^{t}$

     ⇒ $3.7183=(1.05)^{t}$

taking log both sides, we get

         $ln(3.7183)=ln {(1.05)^{t}}$

     ⇒ $1.31327=t\times ln(1.05)$

     ⇒ $1.31327=t\times 0.04879$

    ⇒ $t=26.91$

Therefore,

After $26.91\ years$ the principle amount value will reach to $26400\ dollars$.

Answer 2

Answer: x=26.9

Step-by-step explanation: