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) John had to pay $3488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?
(3) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?
(4) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 3 years.
(5) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?
(6) William had to pay $3710 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.
(9) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?
(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.