Question:
If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4400
Solution And Explanation
Solution
Given,
Amount (A) = $5280
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
$5280 = P (1 + 5% × 4)
⇒ $5280 = P (1 + 5/100 × 4)
⇒ $5280 = P (1 + 5 × 4/100)
⇒ $5280 = P (1 + 20/100)
⇒ $5280 = P (100 + 20/100)
⇒ $5280 = P × 120/100
⇒ P × 120/100 = $5280
⇒ P = 5280/120/100
⇒ P = 5280 × 100/120
⇒ P = 5280 × 100/120
⇒ P = 528000/120
⇒ P = $4400
Thus, the sum borrowed (P) = $4400 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 5280, then the Principal = 100/120 × 5280
= 100 × 5280/120
= 528000/120
= 4400
Thus, Principal = $4400
Thus, the sum borrowed = $4400 Answer
Similar Questions
(1) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 2% simple interest.
(2) What amount will be due after 2 years if John borrowed a sum of $3100 at a 5% simple interest?
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 4 years.
(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 4 years.
(5) William had to pay $3710 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7450 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.
(8) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 3 years.
(10) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.