Question:
How much loan did Joshua borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8280 to clear it?
Correct Answer
$6900
Solution And Explanation
Solution
Given,
Amount (A) = $8280
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
$8280 = P (1 + 4% × 5)
⇒ $8280 = P (1 + 4/100 × 5)
⇒ $8280 = P (1 + 4 × 5/100)
⇒ $8280 = P (1 + 20/100)
⇒ $8280 = P (100 + 20/100)
⇒ $8280 = P × 120/100
⇒ P × 120/100 = $8280
⇒ P = 8280/120/100
⇒ P = 8280 × 100/120
⇒ P = 8280 × 100/120
⇒ P = 828000/120
⇒ P = $6900
Thus, the sum borrowed (P) = $6900 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 8280, then the Principal = 100/120 × 8280
= 100 × 8280/120
= 828000/120
= 6900
Thus, Principal = $6900
Thus, the sum borrowed = $6900 Answer
Similar Questions
(1) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?
(2) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.
(3) If Susan paid $4234 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 3 years.
(5) Joshua had to pay $5194 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 4 years.
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.
(8) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.
(9) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.
(10) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?