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 if Richard borrowed a sum of $3600 at 8% simple interest for 3 years.
(2) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 4 years.
(3) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?
(4) Daniel had to pay $4715 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(6) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 4 years.
(8) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 4 years.
(9) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 6% simple interest?
(10) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.