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) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 7 years.
(2) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 9% simple interest?
(3) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 8 years.
(5) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 3 years.
(7) If Patricia paid $3654 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) If Patricia paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 3% simple interest?
(10) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.