Question

Find out how long it takes a ​$ investment to double if it is invested at compounded . Round to the nearest tenth of a year. Use the formula . A. years B. years C. years D. years

Answer 1

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

$A=P\left(1+\frac{r}{n}\right)^{nt}$

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

$6200=3100\left(1+\frac{0.08}{2}\right)^{2t}$

$\Rightarrow \left(1+0.04\right)^{2t}=6200/3100$

$\Rightarrow 1.04^{2t}=2\\\\\Rightarrow 2t\log_{10}(1.04)=\log_{10}(2)\\ \\\Rightarrow 2t =\frac{\log_{10}(2)}{\log_{10}(1.04)}\\\\\Rightarrow 2t =17.673\\\\\Rightarrow t = 17.673/2=8.8365$

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.