Question:
How much loan did Margaret borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7937.5 to clear it?
Correct Answer
$6350
Solution And Explanation
Solution
Given,
Amount (A) = $7937.5
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
$7937.5 = P (1 + 5% × 5)
⇒ $7937.5 = P (1 + 5/100 × 5)
⇒ $7937.5 = P (1 + 5 × 5/100)
⇒ $7937.5 = P (1 + 25/100)
⇒ $7937.5 = P (100 + 25/100)
⇒ $7937.5 = P × 125/100
⇒ P × 125/100 = $7937.5
⇒ P = 7937.5/125/100
⇒ P = 7937.5 × 100/125
⇒ P = 7937.5 × 100/125
⇒ P = 793750/125
⇒ P = $6350
Thus, the sum borrowed (P) = $6350 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 7937.5, then the Principal = 100/125 × 7937.5
= 100 × 7937.5/125
= 793750/125
= 6350
Thus, Principal = $6350
Thus, the sum borrowed = $6350 Answer
Similar Questions
(1) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 3% simple interest.
(2) How much loan did Jacob borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8800 to clear it?
(3) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 2% simple interest.
(4) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(5) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(6) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.
(7) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 7 years.
(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 7 years.
(10) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.