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 Robert borrowed a sum of $5100 at a rate of 6% simple interest.
(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 7 years.
(3) What amount does John have to pay after 6 years if he takes a loan of $3200 at 9% simple interest?
(4) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.
(6) If Kimberly paid $5394 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?
(8) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 8 years.
(10) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 4% simple interest?