Question:
How much loan did William borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6600 to clear it?
Correct Answer
$5500
Solution And Explanation
Solution
Given,
Amount (A) = $6600
Rate of Simple Interest (R) = 4%
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
$6600 = P (1 + 4% × 5)
⇒ $6600 = P (1 + 4/100 × 5)
⇒ $6600 = P (1 + 4 × 5/100)
⇒ $6600 = P (1 + 20/100)
⇒ $6600 = P (100 + 20/100)
⇒ $6600 = P × 120/100
⇒ P × 120/100 = $6600
⇒ P = 6600/120/100
⇒ P = 6600 × 100/120
⇒ P = 6600 × 100/120
⇒ P = 660000/120
⇒ P = $5500
Thus, the sum borrowed (P) = $5500 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 6600, then the Principal = 100/120 × 6600
= 100 × 6600/120
= 660000/120
= 5500
Thus, Principal = $5500
Thus, the sum borrowed = $5500 Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 6% simple interest?
(3) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.
(4) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9248 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(6) If Kimberly paid $5580 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.
(8) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?
(9) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(10) In how much time a principal of $3150 will amount to $3276 at a simple interest of 2% per annum?