Question:
How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?
Correct Answer
$5600
Solution And Explanation
Solution
Given,
Amount (A) = $6440
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
$6440 = P (1 + 3% × 5)
⇒ $6440 = P (1 + 3/100 × 5)
⇒ $6440 = P (1 + 3 × 5/100)
⇒ $6440 = P (1 + 15/100)
⇒ $6440 = P (100 + 15/100)
⇒ $6440 = P × 115/100
⇒ P × 115/100 = $6440
⇒ P = 6440/115/100
⇒ P = 6440 × 100/115
⇒ P = 6440 × 100/115
⇒ P = 644000/115
⇒ 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 = 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 6440, then the Principal = 100/115 × 6440
= 100 × 6440/115
= 644000/115
= 5600
Thus, Principal = $5600
Thus, the sum borrowed = $5600 Answer
Similar Questions
(1) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 7 years.
(2) In how much time a principal of $3100 will amount to $3875 at a simple interest of 5% per annum?
(3) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6120 to clear the loan, then find the time period of the loan.
(4) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 3% simple interest?
(5) 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.
(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 7 years.
(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 8 years.
(8) If John borrowed $3200 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(9) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5576 to clear the loan, then find the time period of the loan.
(10) In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?