Question:
How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?
Correct Answer
$5350
Solution And Explanation
Solution
Given,
Amount (A) = $6687.5
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
$6687.5 = P (1 + 5% × 5)
⇒ $6687.5 = P (1 + 5/100 × 5)
⇒ $6687.5 = P (1 + 5 × 5/100)
⇒ $6687.5 = P (1 + 25/100)
⇒ $6687.5 = P (100 + 25/100)
⇒ $6687.5 = P × 125/100
⇒ P × 125/100 = $6687.5
⇒ P = 6687.5/125/100
⇒ P = 6687.5 × 100/125
⇒ P = 6687.5 × 100/125
⇒ P = 668750/125
⇒ P = $5350
Thus, the sum borrowed (P) = $5350 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 6687.5, then the Principal = 100/125 × 6687.5
= 100 × 6687.5/125
= 668750/125
= 5350
Thus, Principal = $5350
Thus, the sum borrowed = $5350 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(2) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8856 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 4 years.
(4) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.
(5) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 10% simple interest?
(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 3 years.
(7) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.
(8) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.
(10) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.