Question:
How much loan did Joshua borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7590 to clear it?
Correct Answer
$6900
Solution And Explanation
Solution
Given,
Amount (A) = $7590
Rate of Simple Interest (R) = 2%
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
$7590 = P (1 + 2% × 5)
⇒ $7590 = P (1 + 2/100 × 5)
⇒ $7590 = P (1 + 2 × 5/100)
⇒ $7590 = P (1 + 10/100)
⇒ $7590 = P (100 + 10/100)
⇒ $7590 = P × 110/100
⇒ P × 110/100 = $7590
⇒ P = 7590/110/100
⇒ P = 7590 × 100/110
⇒ P = 7590 × 100/110
⇒ P = 759000/110
⇒ 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 7590, then the Principal = 100/110 × 7590
= 100 × 7590/110
= 759000/110
= 6900
Thus, Principal = $6900
Thus, the sum borrowed = $6900 Answer
Similar Questions
(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 7 years.
(2) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
(3) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.
(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 8 years.
(5) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.
(6) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?
(7) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(8) How much loan did Sharon borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8912.5 to clear it?
(9) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(10) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 4% simple interest?