Question

The simple interest charged on a 65-day loan of $1,290 is $5.75. Find the annual simple interest rate (in percent) for this loan. Round to the nearest tenth of a percent. Use 360 days in 1 year. (Please provide a step-by-step explanation.)

Answer 1

Explanation:

The formula for determining simple interest is expressed as

I = PRT/100

Where

P represents the principal or initial amount invested or collected as a loan.

R represents interest rate.

T represents the duration of time in years before the loan is bald back.

From the information given,

P = 1290

I = 5.75

Since there are 365 days in a year,

t = 65/365 = 0.1781 years

Therefore,

5.75 = (1290 × r × 0.1781)/100

5.75 = 229.749r/100 = 2.29749r

r = 5.75/2.29749

r = 2.5027

Rounding to the nearest percent,

r = 3%

Answer 2

Simple Interest Rate = 2.5%

Explanation:

Simple Interest =(Principal * Rate of Interest * Time) / 100

Principal = $1290

Simple Interest = $5.75

Time = 65 days

Converting it into years assuming 360 days in a year, Time = 65/360 years

`\[5.75 = ((1290 * Rate * (65)/(360)))/(100)\]`

Simplifying,

`\[5.75 *100 = (1290 * Rate * (65)/(360))}\]`

`\[=> Rate=(5.75 * 100 * (360)/(65))/(1290)\]`

`\[=> Rate=2.468%\]`

Rounding off to the nearest tenth of percent,

Rate = 2.5%