Question:
How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?
Correct Answer
$6700
Solution And Explanation
Solution
Given,
Amount (A) = $7370
Rate of Simple Interest (R) = 2%
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
$7370 = P (1 + 2% × 5)
⇒ $7370 = P (1 + 2/100 × 5)
⇒ $7370 = P (1 + 2 × 5/100)
⇒ $7370 = P (1 + 10/100)
⇒ $7370 = P (100 + 10/100)
⇒ $7370 = P × 110/100
⇒ P × 110/100 = $7370
⇒ P = 7370/110/100
⇒ P = 7370 × 100/110
⇒ P = 7370 × 100/110
⇒ P = 737000/110
⇒ P = $6700
Thus, the sum borrowed (P) = $6700 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 7370, then the Principal = 100/110 × 7370
= 100 × 7370/110
= 737000/110
= 6700
Thus, Principal = $6700
Thus, the sum borrowed = $6700 Answer
Similar Questions
(1) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 8 years.
(2) If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 7% simple interest?
(4) If Michael borrowed $3300 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(5) If Paul paid $5264 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 7% simple interest?
(7) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 7% simple interest.
(8) What amount will be due after 2 years if William borrowed a sum of $3250 at a 7% simple interest?
(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 3 years.
(10) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.