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) How much loan did Kevin borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8165 to clear it?
(2) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 7% simple interest.
(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 4 years.
(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.
(5) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 8 years.
(6) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.
(7) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?
(8) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.
(10) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.