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) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 7 years.
(3) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.
(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.
(6) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 8 years.
(7) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?
(8) Donald had to pay $4905 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 3 years.