Question:
How much loan did Richard borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6160 to clear it?
Correct Answer
$5600
Solution And Explanation
Solution
Given,
Amount (A) = $6160
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
$6160 = P (1 + 2% × 5)
⇒ $6160 = P (1 + 2/100 × 5)
⇒ $6160 = P (1 + 2 × 5/100)
⇒ $6160 = P (1 + 10/100)
⇒ $6160 = P (100 + 10/100)
⇒ $6160 = P × 110/100
⇒ P × 110/100 = $6160
⇒ P = 6160/110/100
⇒ P = 6160 × 100/110
⇒ P = 6160 × 100/110
⇒ P = 616000/110
⇒ P = $5600
Thus, the sum borrowed (P) = $5600 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 6160, then the Principal = 100/110 × 6160
= 100 × 6160/110
= 616000/110
= 5600
Thus, Principal = $5600
Thus, the sum borrowed = $5600 Answer
Similar Questions
(1) If Sarah paid $4466 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.
(3) How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?
(4) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(5) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?
(6) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 4 years.
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 4 years.
(8) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(9) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 8 years.
(10) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.