Question:
If William paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3500
Solution And Explanation
Solution
Given,
Amount (A) = $4200
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
$4200 = P (1 + 5% × 4)
⇒ $4200 = P (1 + 5/100 × 4)
⇒ $4200 = P (1 + 5 × 4/100)
⇒ $4200 = P (1 + 20/100)
⇒ $4200 = P (100 + 20/100)
⇒ $4200 = P × 120/100
⇒ P × 120/100 = $4200
⇒ P = 4200/120/100
⇒ P = 4200 × 100/120
⇒ P = 4200 × 100/120
⇒ P = 420000/120
⇒ P = $3500
Thus, the sum borrowed (P) = $3500 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 4200, then the Principal = 100/120 × 4200
= 100 × 4200/120
= 420000/120
= 3500
Thus, Principal = $3500
Thus, the sum borrowed = $3500 Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 3 years.
(3) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.
(4) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(5) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 8% simple interest?
(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 8 years.
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 4 years.
(8) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 7 years.
(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 7 years.
(10) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?