Question

The equations that represent the balance in three different savings accounts x years after 2012,

Answer 1

`A,\text{ B and D}`

Step-by-step explanation:

Here, we want to select the correct option

The general representation of equations that represent a value increase or decrease of a commodity over time is as follows:

`V=I(1+r)^t`

where:

V is the value of the commodity after some years t

I is the purchase or initial value of the commodity

r is the rate of change (if 1 + r is less than 1, then the value of the commodity is decreasing)

t is the number of years after the purchase was made

Now, let us take a look at the options

A) This is correct. It has the highest initial value in the 3

B) This is correct

From what we have:

`\begin{gathered} 1\text{ + r = 1.05} \\ r\text{ = 1.05-1} \\ r\text{ = 0.05} \\ 0.05\text{ = 5/100 which is same as 5\%} \end{gathered}`

C) This is wrong:

`\begin{gathered} 1\text{ + r = }0.85 \\ r\text{ = 0.85-1} \\ r\text{ = -0.15} \\ \end{gathered}`

This is a 15% decrease yearly

D) This is correct

We look at the 1 + r segment

From what we can see, the value in the bracket for A (1.05) is greater than B, which is 1.038