Question

In the following problem, assume simple interest is being calculated and round your answer to the nearest cent. Continental Tools bought a new computer system. They borrowed $54,430 at 7 and 2/3% simple interest for 210 days. Find the interest owed. (Use a 365-day year.)

Answer 1

$2,400.88

Explanation:

Continental Tools bought a new computer system. They borrowed $54,430 at 7 and 2/3% simple interest for 210 days. To find the interest owed, use the simple interest formula.

`\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$I = Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}`

To find the time in years, divide the time in days by 365 (since there are 365 days in a year).

Therefore, the given values are:

• P = $54,430
• r = 7 ²/₃% = 0.07666... = 23/300
• t = 210/365 years

Substitute the given values into the formula and solve for I:

`I=54430 \cdot (23)/(300) \cdot (210)/(365)`

`I= (1251890)/(300) \cdot (210)/(365)`

`I= (262896900)/(109500)`

`I=2400.8849315`

`I=\$2400.88`

Therefore, the interest Continental Tools owed was $2,400.88 (rounded to the nearest cent).

Answer 2

$ 2400

Explanation:

Given:

Principal (P)= $54,430

Rate (R) = 7 and 2/3 % = 7.67 %

Time(T) = 210 days

in terms years

Time(T) =
`(210)/(365)` years = 0.575 year

To find:

Simple Interest (SI)= ?

Formula:

`\boxed{\tt SI= (P*T*R)/(100)}`

Solution:

Substituting value in above formula:

we get

`\tt SI = (54430*0.575*7.67)/(100)`

`\tt SI=(240049.9075)/(100)`

SI=$ 2400.5

in nearest cent $ 2400

Therefore, Interest owned is $ 2400