Question:
How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6812.5 to clear it?
Correct Answer
$5450
Solution And Explanation
Solution
Given,
Amount (A) = $6812.5
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
$6812.5 = P (1 + 5% × 5)
⇒ $6812.5 = P (1 + 5/100 × 5)
⇒ $6812.5 = P (1 + 5 × 5/100)
⇒ $6812.5 = P (1 + 25/100)
⇒ $6812.5 = P (100 + 25/100)
⇒ $6812.5 = P × 125/100
⇒ P × 125/100 = $6812.5
⇒ P = 6812.5/125/100
⇒ P = 6812.5 × 100/125
⇒ P = 6812.5 × 100/125
⇒ P = 681250/125
⇒ P = $5450
Thus, the sum borrowed (P) = $5450 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 6812.5, then the Principal = 100/125 × 6812.5
= 100 × 6812.5/125
= 681250/125
= 5450
Thus, Principal = $5450
Thus, the sum borrowed = $5450 Answer
Similar Questions
(1) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.
(2) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.
(3) 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.
(4) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 4 years.
(6) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?
(7) How much loan did Sharon borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8912.5 to clear it?
(8) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.
(9) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 9% simple interest?
(10) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.