find the annual rate of interest if $5,750 is invested for 40 months and earns interest of $1,825.
find the annual rate of interest if $5,750 is invested for 40 months and earns interest of $1,825.
Answer
Explanation:
Step1: Recall the simple interest formula
The formula for simple interest is ( I = P \times r \times t ), where ( I ) is the interest, ( P ) is the principal amount, ( r ) is the annual interest rate (in decimal), and ( t ) is the time in years.
Step2: Convert time to years
The time is 40 months. Since there are 12 months in a year, ( t=\frac{40}{12}=\frac{10}{3} ) years.
Step3: Rearrange the formula to solve for ( r )
From ( I = P \times r \times t ), we can solve for ( r ) as ( r=\frac{I}{P\times t} ).
Step4: Substitute the given values
We know that ( I = 1825 ), ( P = 5750 ), and ( t=\frac{10}{3} ). Substituting these values into the formula for ( r ): [ r=\frac{1825}{5750\times\frac{10}{3}}=\frac{1825\times3}{5750\times10}=\frac{5475}{57500} = 0.095 ]
Step5: Convert to percentage
To convert the decimal to a percentage, multiply by 100: ( 0.095\times100 = 9.5% ).
Answer:
9.5%