Question

7500 dollars is placed in an account with an annual interest rate of 5.25%. To the nearest tenth of a year, how long will it take for the account value to reach 25200 dollars?

Answer 1

Answer:

After $23.7\ years$ the amount $7500\ dollars$ will reach to $25200\ dollars$.

Step-by-step explanation:

Given that,

                  Principle Amount $(P)$ $=7500\ dollars$

                  Rate of Interest $(R)$ $=5.25$ %

                  Total Amount $(A)$ $= 25200\ dollars$

Now,

        If Principle $=P$ $dollars$, Time $= t$ years, Rate $=R$% $pa$

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

⇒ $A=P(1+\frac{R}{100}) ^{2}$

⇒ $25200=7500(1+\frac{5.25}{100} )^{t}$

⇒ $3.36=(1+0.0525)^{t}$

⇒ $3.36=(1.0525)^{t}$

taking log both sides, we get

⇒ $ln(3.36)=ln(1.0525^{t})$

⇒ $1.21194=t\times ln(1.0525)$

⇒ $1.21194=t\times 0.05117$

⇒ $t=23.7$

Therefore,

After $23.7\ years$ the amount $7500\ dollars$ will reach to $25200\ dollars$.