Question:
How much loan did Michelle borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8687.5 to clear it?
Correct Answer
$6950
Solution And Explanation
Solution
Given,
Amount (A) = $8687.5
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
$8687.5 = P (1 + 5% × 5)
⇒ $8687.5 = P (1 + 5/100 × 5)
⇒ $8687.5 = P (1 + 5 × 5/100)
⇒ $8687.5 = P (1 + 25/100)
⇒ $8687.5 = P (100 + 25/100)
⇒ $8687.5 = P × 125/100
⇒ P × 125/100 = $8687.5
⇒ P = 8687.5/125/100
⇒ P = 8687.5 × 100/125
⇒ P = 8687.5 × 100/125
⇒ P = 868750/125
⇒ P = $6950
Thus, the sum borrowed (P) = $6950 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 8687.5, then the Principal = 100/125 × 8687.5
= 100 × 8687.5/125
= 868750/125
= 6950
Thus, Principal = $6950
Thus, the sum borrowed = $6950 Answer
Similar Questions
(1) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?
(2) How much loan did Mary borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6312.5 to clear it?
(3) How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?
(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.
(5) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 7 years.
(7) In how much time a principal of $3150 will amount to $3402 at a simple interest of 2% per annum?
(8) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 4 years.
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 3 years.