Question:
How much loan did Lisa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7562.5 to clear it?
Correct Answer
$6050
Solution And Explanation
Solution
Given,
Amount (A) = $7562.5
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
$7562.5 = P (1 + 5% × 5)
⇒ $7562.5 = P (1 + 5/100 × 5)
⇒ $7562.5 = P (1 + 5 × 5/100)
⇒ $7562.5 = P (1 + 25/100)
⇒ $7562.5 = P (100 + 25/100)
⇒ $7562.5 = P × 125/100
⇒ P × 125/100 = $7562.5
⇒ P = 7562.5/125/100
⇒ P = 7562.5 × 100/125
⇒ P = 7562.5 × 100/125
⇒ P = 756250/125
⇒ P = $6050
Thus, the sum borrowed (P) = $6050 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 7562.5, then the Principal = 100/125 × 7562.5
= 100 × 7562.5/125
= 756250/125
= 6050
Thus, Principal = $6050
Thus, the sum borrowed = $6050 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7783 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 4 years.
(3) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 8 years.
(4) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.
(5) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.
(6) How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?
(7) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 6% simple interest?
(9) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.
(10) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.