Question:
How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6267.5 to clear it?
Correct Answer
$5450
Solution And Explanation
Solution
Given,
Amount (A) = $6267.5
Rate of Simple Interest (R) = 3%
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
$6267.5 = P (1 + 3% × 5)
⇒ $6267.5 = P (1 + 3/100 × 5)
⇒ $6267.5 = P (1 + 3 × 5/100)
⇒ $6267.5 = P (1 + 15/100)
⇒ $6267.5 = P (100 + 15/100)
⇒ $6267.5 = P × 115/100
⇒ P × 115/100 = $6267.5
⇒ P = 6267.5/115/100
⇒ P = 6267.5 × 100/115
⇒ P = 6267.5 × 100/115
⇒ P = 626750/115
⇒ 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 6267.5, then the Principal = 100/115 × 6267.5
= 100 × 6267.5/115
= 626750/115
= 5450
Thus, Principal = $5450
Thus, the sum borrowed = $5450 Answer
Similar Questions
(1) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?
(2) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.
(3) How much loan did Ryan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8690 to clear it?
(4) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $8704 to clear the loan, then find the time period of the loan.
(5) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.
(6) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.
(8) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 4% simple interest?
(9) If John borrowed $3200 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.