Question:
How much loan did Jessica borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7187.5 to clear it?
Correct Answer
$5750
Solution And Explanation
Solution
Given,
Amount (A) = $7187.5
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
$7187.5 = P (1 + 5% × 5)
⇒ $7187.5 = P (1 + 5/100 × 5)
⇒ $7187.5 = P (1 + 5 × 5/100)
⇒ $7187.5 = P (1 + 25/100)
⇒ $7187.5 = P (100 + 25/100)
⇒ $7187.5 = P × 125/100
⇒ P × 125/100 = $7187.5
⇒ P = 7187.5/125/100
⇒ P = 7187.5 × 100/125
⇒ P = 7187.5 × 100/125
⇒ P = 718750/125
⇒ P = $5750
Thus, the sum borrowed (P) = $5750 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 7187.5, then the Principal = 100/125 × 7187.5
= 100 × 7187.5/125
= 718750/125
= 5750
Thus, Principal = $5750
Thus, the sum borrowed = $5750 Answer
Similar Questions
(1) If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(3) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(4) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(5) If Richard paid $3888 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.
(8) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
(9) If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 8% simple interest?