Question:
How much loan did Melissa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9187.5 to clear it?
Correct Answer
$7350
Solution And Explanation
Solution
Given,
Amount (A) = $9187.5
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
$9187.5 = P (1 + 5% × 5)
⇒ $9187.5 = P (1 + 5/100 × 5)
⇒ $9187.5 = P (1 + 5 × 5/100)
⇒ $9187.5 = P (1 + 25/100)
⇒ $9187.5 = P (100 + 25/100)
⇒ $9187.5 = P × 125/100
⇒ P × 125/100 = $9187.5
⇒ P = 9187.5/125/100
⇒ P = 9187.5 × 100/125
⇒ P = 9187.5 × 100/125
⇒ P = 918750/125
⇒ P = $7350
Thus, the sum borrowed (P) = $7350 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 9187.5, then the Principal = 100/125 × 9187.5
= 100 × 9187.5/125
= 918750/125
= 7350
Thus, Principal = $7350
Thus, the sum borrowed = $7350 Answer
Similar Questions
(1) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.
(2) What amount does David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?
(3) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 2% simple interest.
(4) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
(5) If Patricia paid $3402 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) If William borrowed $3500 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 4 years.
(9) How much loan did Timothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8510 to clear it?
(10) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?