Question

If I have $875 I plan to put in the bank for 3 months, and the annual interest rate is 5.5%... A. What is the formula you would use to find the amount of interest earned? B. Label each variable in the formula with the number you will use to find your an

Answer 1

Compound interest: `P[color(white)(.)(1+(x%)/12)^n-1]`

Simple interest: `(nPx%)/12`

See explanation

Explanation:

BANKS NORMALLY GIVE COMPOUND INTEREST.

`color(blue)("Compound interest")`

The annual interest will have to be divided by 12 and applied to the related months (interest rates change).

`color(brown)("Let the principle sum be "P)`

`color(brown)("Let "x%" be the annual interest proportioned monthly.")`

`color(brown)("Let "n" be the count of the calculation cycle (months)")`

So we have

`P(1+(x%)/12)^(n) color(white)("d") ->color(white)("d") $875(1+5.5/(12xx100))^3`

`color(white)("ddddddddddddd") ->color(white)("d") $875(1205.5/1200)^3=$887.0864.....`

`$887.09` to 2 decimal places
`ul($875.00larr" Subtract")`
`$color(white)("d")12.09 larr" Interest to 2 dp"`

As the interest earned is the difference we have

`P(1+(x%)/12)^(n) -Pcolor(white)("ddd")->color(white)("ddd")P[color(white)(.)(1+(x%)/12)^n-1]`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Simple interest") larr" Not realistic!"`

Building it

`P + P((x%)/12) +P((x%)/12)+P((x%)/12)`

Factor out The `P`

`P(1+(3x%)/12) larr" Everything"`

`P(1+(3x%)/12)-P larr" Just the interest"`

`cancel(P)+P(3x%)/12-cancel(P)`

`(3Px%)/12 larr "For 3 months" = (cancel(3)^1xx$875xx5.5)/(cancel(1200)^400) = $12.03` to 2 dp

`(nPx%)/12 larr" Generic case"`