Question:
If Margaret paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4350
Solution And Explanation
Solution
Given,
Amount (A) = $5220
Rate of Simple Interest (R) = 5%
Time (T) = 4 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
$5220 = P (1 + 5% × 4)
⇒ $5220 = P (1 + 5/100 × 4)
⇒ $5220 = P (1 + 5 × 4/100)
⇒ $5220 = P (1 + 20/100)
⇒ $5220 = P (100 + 20/100)
⇒ $5220 = P × 120/100
⇒ P × 120/100 = $5220
⇒ P = 5220/120/100
⇒ P = 5220 × 100/120
⇒ P = 5220 × 100/120
⇒ P = 522000/120
⇒ P = $4350
Thus, the sum borrowed (P) = $4350 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
Calculation of the Amount
Since, in the question, time = 4 years
So, we need to calculate the simple interest for the given time period, which is 4 years
Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year
= 4 × 5 = 20
Thus, simple interest for 4 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 5220, then the Principal = 100/120 × 5220
= 100 × 5220/120
= 522000/120
= 4350
Thus, Principal = $4350
Thus, the sum borrowed = $4350 Answer
Similar Questions
(1) If Charles paid $4680 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(3) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5712 to clear the loan, then find the time period of the loan.
(4) If Paul paid $5640 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.
(6) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.
(7) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 7% simple interest?
(8) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.
(9) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 6% simple interest?
(10) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 4 years.