Question:
If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3400
Solution And Explanation
Solution
Given,
Amount (A) = $3672
Rate of Simple Interest (R) = 2%
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
$3672 = P (1 + 2% × 4)
⇒ $3672 = P (1 + 2/100 × 4)
⇒ $3672 = P (1 + 2 × 4/100)
⇒ $3672 = P (1 + 8/100)
⇒ $3672 = P (100 + 8/100)
⇒ $3672 = P × 108/100
⇒ P × 108/100 = $3672
⇒ P = 3672/108/100
⇒ P = 3672 × 100/108
⇒ P = 3672 × 100/108
⇒ P = 367200/108
⇒ P = $3400
Thus, the sum borrowed (P) = $3400 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 3672, then the Principal = 100/108 × 3672
= 100 × 3672/108
= 367200/108
= 3400
Thus, Principal = $3400
Thus, the sum borrowed = $3400 Answer
Similar Questions
(1) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(2) If Emily paid $5510 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 9% simple interest?
(4) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 4 years.
(5) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8528 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?
(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 4 years.
(8) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 7 years.
(9) How much loan did Amanda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7865 to clear it?
(10) What amount does James have to pay after 5 years if he takes a loan of $3000 at 2% simple interest?