Question:
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.
Correct Answer
$3950
Solution And Explanation
Solution
Given,
Amount (A) = $4740
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
$4740 = P (1 + 5% × 4)
⇒ $4740 = P (1 + 5/100 × 4)
⇒ $4740 = P (1 + 5 × 4/100)
⇒ $4740 = P (1 + 20/100)
⇒ $4740 = P (100 + 20/100)
⇒ $4740 = P × 120/100
⇒ P × 120/100 = $4740
⇒ P = 4740/120/100
⇒ P = 4740 × 100/120
⇒ P = 4740 × 100/120
⇒ P = 474000/120
⇒ P = $3950
Thus, the sum borrowed (P) = $3950 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 4740, then the Principal = 100/120 × 4740
= 100 × 4740/120
= 474000/120
= 3950
Thus, Principal = $3950
Thus, the sum borrowed = $3950 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.
(2) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(3) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 6% simple interest?
(4) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 8 years.
(7) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 3 years.
(8) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.
(9) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 3% simple interest?
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 4 years.