Question:
If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3000
Solution And Explanation
Solution
Given,
Amount (A) = $3240
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
$3240 = P (1 + 2% × 4)
⇒ $3240 = P (1 + 2/100 × 4)
⇒ $3240 = P (1 + 2 × 4/100)
⇒ $3240 = P (1 + 8/100)
⇒ $3240 = P (100 + 8/100)
⇒ $3240 = P × 108/100
⇒ P × 108/100 = $3240
⇒ P = 3240/108/100
⇒ P = 3240 × 100/108
⇒ P = 3240 × 100/108
⇒ P = 324000/108
⇒ P = $3000
Thus, the sum borrowed (P) = $3000 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 3240, then the Principal = 100/108 × 3240
= 100 × 3240/108
= 324000/108
= 3000
Thus, Principal = $3000
Thus, the sum borrowed = $3000 Answer
Similar Questions
(1) How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?
(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.
(3) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 4% simple interest?
(4) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 8 years.
(6) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6109 to clear the loan, then find the time period of the loan.
(7) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 7 years.
(9) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 3 years.