Question:
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?
Correct Answer
$5050
Solution And Explanation
Solution
Given,
Amount (A) = $6312.5
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
$6312.5 = P (1 + 5% × 5)
⇒ $6312.5 = P (1 + 5/100 × 5)
⇒ $6312.5 = P (1 + 5 × 5/100)
⇒ $6312.5 = P (1 + 25/100)
⇒ $6312.5 = P (100 + 25/100)
⇒ $6312.5 = P × 125/100
⇒ P × 125/100 = $6312.5
⇒ P = 6312.5/125/100
⇒ P = 6312.5 × 100/125
⇒ P = 6312.5 × 100/125
⇒ P = 631250/125
⇒ P = $5050
Thus, the sum borrowed (P) = $5050 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 6312.5, then the Principal = 100/125 × 6312.5
= 100 × 6312.5/125
= 631250/125
= 5050
Thus, Principal = $5050
Thus, the sum borrowed = $5050 Answer
Similar Questions
(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.
(2) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.
(3) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7700 to clear it?
(4) What amount will be due after 2 years if James borrowed a sum of $3000 at a 9% simple interest?
(5) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.
(6) How much loan did Margaret borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7620 to clear it?
(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.
(8) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?
(9) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
(10) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.