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A finance company charges $55 simple interest on a sum of money which is borrowed for five months. Given that the rate of interest is 12% per annum, find the original sum of money.

A finance company charges $55 \$ 55 simple interest on a sum of money which is borrowed for five months. Given that the rate of interest is 12% 12 \% per annum, find the original sum of money.

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Full solution

Q. A finance company charges $55 \$ 55 simple interest on a sum of money which is borrowed for five months. Given that the rate of interest is 12% 12 \% per annum, find the original sum of money.
  1. Identify Known Values: Identify the known values from the problem.\newlineSimple interest charged I=$55I = \$55\newlineTime period T=5T = 5 months (which is 512\frac{5}{12} years)\newlineAnnual interest rate R=12%R = 12\%\newlineWe need to find the principal amount PP.
  2. Write Formula for Simple Interest: Write down the formula for simple interest.\newlineThe formula for simple interest is I=P×R×TI = P \times R \times T, where II is the interest, PP is the principal amount, RR is the rate of interest per year, and TT is the time in years.
  3. Convert Time Period to Years: Convert the time period from months to years because the interest rate is per annum.\newlineT=5T = 5 months =512= \frac{5}{12} years
  4. Convert Annual Interest Rate: Convert the annual interest rate into a decimal for calculation.\newlineR=12%R = 12\% per annum =12100=0.12= \frac{12}{100} = 0.12
  5. Rearrange Formula for Principal: Rearrange the simple interest formula to solve for the principal amount PP.P=IR×TP = \frac{I}{R \times T}
  6. Substitute Known Values: Substitute the known values into the rearranged formula to calculate the principal. \newlineP=$550.12×(512)P = \frac{\$55}{0.12 \times (\frac{5}{12})}
  7. Perform Calculation: Perform the calculation.\newlineP=extextdollar550.12×512P = \frac{ ext{ extdollar}55}{0.12 \times \frac{5}{12}}\newlineP=extextdollar550.12×0.4167P = \frac{ ext{ extdollar}55}{0.12 \times 0.4167}\newlineP=extextdollar550.05P = \frac{ ext{ extdollar}55}{0.05}\newlineP= extdollar1100P = \text{ extdollar}1100

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