Question:
How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6540 to clear it?
Correct Answer
$5450
Solution And Explanation
Solution
Given,
Amount (A) = $6540
Rate of Simple Interest (R) = 4%
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
$6540 = P (1 + 4% × 5)
⇒ $6540 = P (1 + 4/100 × 5)
⇒ $6540 = P (1 + 4 × 5/100)
⇒ $6540 = P (1 + 20/100)
⇒ $6540 = P (100 + 20/100)
⇒ $6540 = P × 120/100
⇒ P × 120/100 = $6540
⇒ P = 6540/120/100
⇒ P = 6540 × 100/120
⇒ P = 6540 × 100/120
⇒ P = 654000/120
⇒ 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 6540, then the Principal = 100/120 × 6540
= 100 × 6540/120
= 654000/120
= 5450
Thus, Principal = $5450
Thus, the sum borrowed = $5450 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 4 years.
(3) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 7% simple interest?
(4) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 3 years.
(5) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(6) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.
(7) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.
(9) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 8 years.
(10) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.