Question:
If Joseph paid $4292 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3700
Solution And Explanation
Solution
Given,
Amount (A) = $4292
Rate of Simple Interest (R) = 4%
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
$4292 = P (1 + 4% × 4)
⇒ $4292 = P (1 + 4/100 × 4)
⇒ $4292 = P (1 + 4 × 4/100)
⇒ $4292 = P (1 + 16/100)
⇒ $4292 = P (100 + 16/100)
⇒ $4292 = P × 116/100
⇒ P × 116/100 = $4292
⇒ P = 4292/116/100
⇒ P = 4292 × 100/116
⇒ P = 4292 × 100/116
⇒ P = 429200/116
⇒ P = $3700
Thus, the sum borrowed (P) = $3700 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 16
Thus, simple interest for 4 years = 16
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 16 = 116
Calculation of the Principal
Now,
∵ If the Amount is 116, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/116
∴ If the Amount is 4292, then the Principal = 100/116 × 4292
= 100 × 4292/116
= 429200/116
= 3700
Thus, Principal = $3700
Thus, the sum borrowed = $3700 Answer
Similar Questions
(1) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 4 years.
(2) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.
(3) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(4) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.
(5) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 7 years.
(7) How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?
(8) If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 9% simple interest?
(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 8 years.