Question

Ana agrees to pay 8% simple interest per year for a computer over 3 years

PART A : if ana pays a total of 312 in interest per year, how much money did the computer cost

PART B : if the simple interest rate were 5% instead of 8% per year, how much would ana save in interest?

Please help

Answer 1

PART A: $1,300.

PART B: $117

Explanation:

PART A:

Let P be the principal amount (the cost of the computer).

The formula for simple interest is S.I.
`= (P*t*r)/(100)`

where S.I. is the interest, P is the principal, r is the interest rate, and t is the time in years.

We know that Ana pays a total of $312 in interest per year so we can write:

312 = P * 8/100 * 3

Simplifying, we get:

P =
`(312)/(0.08 * 3)=1300`

Therefore, the cost of the computer was $1,300.

PART B:

Let P be the principal amount (the cost of the computer).

The formula for simple interest is I = P * r * t, where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

If the interest rate were 5% instead of 8%, the annual interest would be 0.05P. Therefore, the total interest paid over three years would be:

`I_(5per)= P * 0.05 * 3 = 0.15P`

The difference in interest paid is the subtraction of the total interest paid at 5% from the total interest paid at 8%:

`I_(diff )= P * (0.08 - 0.05) * 3 = 0.09P`

Therefore, the amount that Ana would save in interest if the interest rate were 5% instead of 8% is:

`I_(diff)= 0.09P`

Substituting P = 1300 from Part A, we get:

`I_(diff)` = 0.09 * 1300 = 117

So Ana would save $117 in interest if the interest rate were 5% instead of 8%.