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) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.
(2) How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?
(3) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?
(4) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.
(5) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
(7) Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.
(9) Calculate the amount due if Susan borrowed a sum of $3650 at 8% simple interest for 4 years.
(10) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.