Question:
How much loan did Mark borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8000 to clear it?
Correct Answer
$6400
Solution And Explanation
Solution
Given,
Amount (A) = $8000
Rate of Simple Interest (R) = 5%
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
$8000 = P (1 + 5% × 5)
⇒ $8000 = P (1 + 5/100 × 5)
⇒ $8000 = P (1 + 5 × 5/100)
⇒ $8000 = P (1 + 25/100)
⇒ $8000 = P (100 + 25/100)
⇒ $8000 = P × 125/100
⇒ P × 125/100 = $8000
⇒ P = 8000/125/100
⇒ P = 8000 × 100/125
⇒ P = 8000 × 100/125
⇒ P = 800000/125
⇒ P = $6400
Thus, the sum borrowed (P) = $6400 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 = 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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 8000, then the Principal = 100/125 × 8000
= 100 × 8000/125
= 800000/125
= 6400
Thus, Principal = $6400
Thus, the sum borrowed = $6400 Answer
Similar Questions
(1) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11222 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.
(3) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.
(4) What amount does David have to pay after 5 years if he takes a loan of $3400 at 4% simple interest?
(5) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 8 years.
(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 4 years.
(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 7 years.
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 7 years.
(9) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.
(10) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?