Respuesta :
Answer:
(A) 8.8 years
Step-by-step explanation:
Given that the principal amount = $ 3100
Rate of compound interest = 8% compounded semiannually.
The given formula is
[tex]A=P\left(1+\frac{r}{n}\right)^{nt}[/tex]
Where A is the final amount, P is the principal amount, r is the rate of compound interest, t is the time and n is the number of times per year the interest is compounded.
From the given condition,
P=$3100
r= 8%=0.08 compounded semiannually
n=2
A=2 x 3100=$ 6200.
Put all these in the given formula to get the required time, we have
[tex]6200=3100\left(1+\frac{0.08}{2}\right)^{2t}[/tex]
[tex]\Rightarrow \left(1+0.04\right)^{2t}=6200/3100[/tex]
[tex]\Rightarrow 1.04^{2t}=2\\\\\Rightarrow 2t\log_{10}(1.04)=\log_{10}(2)\\ \\\Rightarrow 2t =\frac{\log_{10}(2)}{\log_{10}(1.04)}\\\\\Rightarrow 2t =17.673\\\\\Rightarrow t = 17.673/2=8.8365\\[/tex]
On rounding to the nearest tenth of a year, t=8.8 years.
So, the invested amount will be double in 8.8 years.
Hence, option (A) is correct.
