Question

Rita borrowed $1,600 at 12% interest for 90 days. How much interest did she pay on the loan? a. $1640 b. $48 c. $192 d. $80

Answer 1

`£$48tob`

Explanation:

`"simple interest (I) is calculated as"`

`•color(white)(x)I=PRT`

`"where P is the amount borrowed"`

`"R is the rate of interest"`

`"T is the time in years"`

`"here "P=$1600`

`R=12%=12/100=0.12`

`T=90/365larrcolor(blue)"in fraction of year"`

`I=(1600xx0.12xx90)/365`

`color(white)(I)=$47.34~~$48tob`

Answer 2

You do not state if simple or compound interest and you do not state the calculation time cycle.

`"Option (a) at "$1640`

Explanation:

Assuming compound interest

Compound interest is normally calculated per month. Some months have more days than others so within this context 90 days gives us a problem.

Adjust the calculation I used to that which you think is appropriate. If necessary!

For 24 day months we have: `90-: 24 = 3.75` so lets say 4 calculation cycles.

The interest is spread over all the months in a year so each calculation cycle (monthly) applies `("12%")/12`

`y=P(1+(x%)/12)^(12n)` where `P` is the principle sum and `n` is the count in years. So in this case (4 months) `n=4/12=1/3` giving:

`y=$1600(1+12/1200)^(12xx1/3)`

`y=$1600xx(1212/1200)^4 = $1664.97` to 2 decimal places.

Of the options available `$1640` is very close so I choose that one.

Ans `->" option (a) at "$1640`

`color(blue)("You will have to adjust the cycle time to suits for the exact situation")`