Question:
How much loan did Charles borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6785 to clear it?
Correct Answer
$5900
Solution And Explanation
Solution
Given,
Amount (A) = $6785
Rate of Simple Interest (R) = 3%
Time (T) = 5 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
$6785 = P (1 + 3% × 5)
⇒ $6785 = P (1 + 3/100 × 5)
⇒ $6785 = P (1 + 3 × 5/100)
⇒ $6785 = P (1 + 15/100)
⇒ $6785 = P (100 + 15/100)
⇒ $6785 = P × 115/100
⇒ P × 115/100 = $6785
⇒ P = 6785/115/100
⇒ P = 6785 × 100/115
⇒ P = 6785 × 100/115
⇒ P = 678500/115
⇒ P = $5900
Thus, the sum borrowed (P) = $5900 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
Calculation of the Amount
Since, in the question, time = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 3 = 15
Thus, simple interest for 5 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 6785, then the Principal = 100/115 × 6785
= 100 × 6785/115
= 678500/115
= 5900
Thus, Principal = $5900
Thus, the sum borrowed = $5900 Answer
Similar Questions
(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 3 years.
(2) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.
(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.
(5) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?
(7) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 9% simple interest?
(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?
(9) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(10) If Mary borrowed $3050 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.