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) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 8 years.
(2) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.
(3) In how much time a principal of $3150 will amount to $3465 at a simple interest of 2% per annum?
(4) If Nancy paid $4814 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?
(6) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
(7) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 8 years.
(9) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 10% simple interest?
(10) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.