Question:
How much loan did Robert borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6120 to clear it?
Correct Answer
$5100
Solution And Explanation
Solution
Given,
Amount (A) = $6120
Rate of Simple Interest (R) = 4%
Time (T) = 5 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
$6120 = P (1 + 4% × 5)
⇒ $6120 = P (1 + 4/100 × 5)
⇒ $6120 = P (1 + 4 × 5/100)
⇒ $6120 = P (1 + 20/100)
⇒ $6120 = P (100 + 20/100)
⇒ $6120 = P × 120/100
⇒ P × 120/100 = $6120
⇒ P = 6120/120/100
⇒ P = 6120 × 100/120
⇒ P = 6120 × 100/120
⇒ P = 612000/120
⇒ P = $5100
Thus, the sum borrowed (P) = $5100 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 = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 4 = 20
Thus, simple interest for 5 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 6120, then the Principal = 100/120 × 6120
= 100 × 6120/120
= 612000/120
= 5100
Thus, Principal = $5100
Thus, the sum borrowed = $5100 Answer
Similar Questions
(1) If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?
(3) If Charles paid $4524 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) Robert had to pay $3565 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) What amount does William have to pay after 5 years if he takes a loan of $3500 at 4% simple interest?
(6) How much loan did James borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5500 to clear it?
(7) How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?
(8) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.
(9) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.
(10) Anthony had to pay $4687 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.