Question

Find the time. Round to the nearest day given the following:Principal: $74,000Rate: 9.5%Interest: $2343.33

Answer 1

Step-by-step explanation

Simple Interest is calculated using the following formula:

`I=\text{PRT}`

where P is the principal ( initial amount)

R is the rate ( in decimal)

T is the time ( in years)

so

Step 1

Let

`\begin{gathered} P=74000 \\ \text{rate}=\text{ 9.5\% =9.5/100= 0.095} \\ T=t\text{ ( unknown)} \\ \text{Interest}=\text{ 2343.33} \end{gathered}`

now, replace

`\begin{gathered} I=\text{PRT} \\ 2343.33=74000\cdot0.095\cdot t \\ 2343.33=7030t \\ \text{divide both sides by 7030} \\ (2343.33)/(7030)=(7030t)/(7030) \\ 0.3333=t\text{ } \end{gathered}`

so, the time is 0.333 years

Step 2

convert 0.333 years into days

`1\text{ year }\Rightarrow365\text{ days}`

so

`\begin{gathered} 0.333years(\frac{365}{1\text{ year}})=121.66 \\ \text{rounded} \\ 122\text{ days} \end{gathered}`

therefore, the answer is

122 days