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) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 8 years.
(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 7 years.
(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 3 years.
(4) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 3 years.
(5) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.
(7) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(8) What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?
(9) If William paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) 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.