Question:
Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
Correct Answer
$3700
Solution And Explanation
Solution
Given,
Amount (A) = $4255
Rate of Simple Interest (R) = 5%
Time (T) = 3 years
Thus, Principal (P) = ?
Method (1) Using Formula
Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given
Formula to find the Principal (P)
Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)
⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]
⇒ A = P (1 + RT)
Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given
In the given question, we need to find the Principal (P)
Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get
$4255 = P (1 + 5% × 3)
⇒ $4255 = P (1 + 5/100 × 3)
⇒ $4255 = P (1 + 5 × 3/100)
⇒ $4255 = P (1 + 15/100)
⇒ $4255 = P (100 + 15/100)
⇒ $4255 = P × 115/100
⇒ P × 115/100 = $4255
⇒ P = 4255/115/100
⇒ P = 4255 × 100/115
⇒ P = 4255 × 100/115
⇒ P = 425500/115
⇒ P = $3700
Thus, the sum borrowed (P) = $3700 Answer
Method (1) Using Unitary Method
Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given
Calculation of the Simple Interest
Let, the principal = 100
Here, since rate of simple interest = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
Calculation of the Amount
Since, in the question, time = 3 years
So, we need to calculate the simple interest for the given time period, which is 3 years
Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year
= 3 × 5 = 15
Thus, simple interest for 3 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 4255, then the Principal = 100/115 × 4255
= 100 × 4255/115
= 425500/115
= 3700
Thus, Principal = $3700
Thus, the sum borrowed = $3700 Answer
Similar Questions
(1) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 3 years.
(2) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(4) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 7 years.
(5) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(6) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.
(7) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8024 to clear the loan, then find the time period of the loan.
(8) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(9) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 3 years.