Question:
How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?
Correct Answer
$7950
Solution And Explanation
Solution
Given,
Amount (A) = $9937.5
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
$9937.5 = P (1 + 5% × 5)
⇒ $9937.5 = P (1 + 5/100 × 5)
⇒ $9937.5 = P (1 + 5 × 5/100)
⇒ $9937.5 = P (1 + 25/100)
⇒ $9937.5 = P (100 + 25/100)
⇒ $9937.5 = P × 125/100
⇒ P × 125/100 = $9937.5
⇒ P = 9937.5/125/100
⇒ P = 9937.5 × 100/125
⇒ P = 9937.5 × 100/125
⇒ P = 993750/125
⇒ P = $7950
Thus, the sum borrowed (P) = $7950 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 9937.5, then the Principal = 100/125 × 9937.5
= 100 × 9937.5/125
= 993750/125
= 7950
Thus, Principal = $7950
Thus, the sum borrowed = $7950 Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 4 years.
(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 8 years.
(4) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 7% simple interest?
(6) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 7 years.
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 7 years.
(8) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 9% simple interest?
(9) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 7 years.