Question:
How much loan did Edward borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8740 to clear it?
Correct Answer
$7600
Solution And Explanation
Solution
Given,
Amount (A) = $8740
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
$8740 = P (1 + 3% × 5)
⇒ $8740 = P (1 + 3/100 × 5)
⇒ $8740 = P (1 + 3 × 5/100)
⇒ $8740 = P (1 + 15/100)
⇒ $8740 = P (100 + 15/100)
⇒ $8740 = P × 115/100
⇒ P × 115/100 = $8740
⇒ P = 8740/115/100
⇒ P = 8740 × 100/115
⇒ P = 8740 × 100/115
⇒ P = 874000/115
⇒ P = $7600
Thus, the sum borrowed (P) = $7600 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 8740, then the Principal = 100/115 × 8740
= 100 × 8740/115
= 874000/115
= 7600
Thus, Principal = $7600
Thus, the sum borrowed = $7600 Answer
Similar Questions
(1) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 4 years.
(2) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(3) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 9% simple interest?
(4) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.
(5) How much loan did Margaret borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7620 to clear it?
(6) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 8 years.
(8) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 6% simple interest?
(9) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.