Question:
How much loan did Susan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6780 to clear it?
Correct Answer
$5650
Solution And Explanation
Solution
Given,
Amount (A) = $6780
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
$6780 = P (1 + 4% × 5)
⇒ $6780 = P (1 + 4/100 × 5)
⇒ $6780 = P (1 + 4 × 5/100)
⇒ $6780 = P (1 + 20/100)
⇒ $6780 = P (100 + 20/100)
⇒ $6780 = P × 120/100
⇒ P × 120/100 = $6780
⇒ P = 6780/120/100
⇒ P = 6780 × 100/120
⇒ P = 6780 × 100/120
⇒ P = 678000/120
⇒ P = $5650
Thus, the sum borrowed (P) = $5650 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 6780, then the Principal = 100/120 × 6780
= 100 × 6780/120
= 678000/120
= 5650
Thus, Principal = $5650
Thus, the sum borrowed = $5650 Answer
Similar Questions
(1) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 7 years.
(3) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.
(4) If Betty paid $4760 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.
(6) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(7) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.
(10) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.