Question

The annual rate, r , compounded annually, it takes for$1 dollar to grow to B dollars in 3 years is given by the formula B=(1+r)^3 . Find the rate necessary for a dollar to double in 3 years.

Give your answer to one decimal place, if required.

Answer 1

Answer:

r=26.0%

Step-by-step explanation:

If with the annual rate, r , compounded annually, it takes for$1 dollar to grow to B dollars in 3 years is given by the formula

$B=(1+r)^3$

Then, the general formula for the amount after 1 dollar is accumulated for n years at a rate r is

$A= 1*(1+r)^n$

the double of 1 dollar is 2 dollars

the time given is 3 years

Therefore,

$2=1*(1+r)^3$

we make r the subject of the formula as follows

$2^{(\frac{1}{3})} =(1+r)\\\\r=2^{(\frac{1}{3})}-1\\\\r=1.25992105-1\\r=0.259921$

r=25.9921%

to 1 decimal place

r=26.0%