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) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 10% simple interest?
(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.
(4) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 5% simple interest?
(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 4 years.
(6) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.
(7) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?
(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.
(9) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.