Question

Question #8cdcd

Answer 1

the interest rate = 2.75%/year

Explanation:

Equation:
r = (1/t)(A/P - 1)

Solving our equation:
r = `(1/1)((2260.5/2200) - 1)`= 0.0275
r = `0.0275`

Converting r decimal to R a percentage
R = `0.0275 * 100`
R = `2.75%` per year

The interest rate required to get a total amount, principal plus interest, of $2,260.50 from simple interest on a principal of $2,200.00 over 1 years is 2.75% per year.

Answer 2

`2.76%`

Full explanation given.

Explanation:

`color(purple)("With practice you should be able to work these out in just a few")` `color(purple)("lines.")`

The amount of interest earned is:

`$2260.50`
`ul($2200.00 larr" Subtract")`
`$color(white)("dd")60.50`

So as a fraction we have

`("amount gained")/("original amount") ->($60.50)/($2200.00)`

`color(blue)("First principle method")`

Percentage is just a fraction. However it is a special fraction in that the bottom number (denominator) is always fixed at 100.

With what follows notice the way the units of measurement ($) cancel out and we are left with just numbers.

So we need to change `(cancel($)60.50)/(cancel($)2200.00)` into:

`color(white)("ddddddddddddddd")("some number")/100`

How can we change 2200 into 100?

We can do this: `ubrace(2200xx1/2200)xx100=100`
`color(white)("ddddddddddddd")` becomes 1

In a fraction, for multiply and divide, what we do to the bottom we also do to the top. So we also have to multiply the top in the same way.

`60.50xx1/2200xx100 = 2.75`

`color(brown)("Putting it all back together")`

`(cancel($)60.50)/(cancel($)2200.00) -=2.75/100`

Note that `2.75/100` is the same as `2.75xx1/100` is the same as `2.75%`

So `%` is the same as `color(white)("ddd")xx1/100`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Shortcut method ")`

`color(brown)("In common with all shortcut methods, they are just")` `color(brown)("remembering what happens with first principles")`

`(cancel($)60.50)/(cancel($)2200.00)->(60.5-:2200)xx100`

And then 'stick' a % on the end `->2.75%`