Question:
How much loan did Robert borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5610 to clear it?
Correct Answer
$5100
Solution And Explanation
Solution
Given,
Amount (A) = $5610
Rate of Simple Interest (R) = 2%
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
$5610 = P (1 + 2% × 5)
⇒ $5610 = P (1 + 2/100 × 5)
⇒ $5610 = P (1 + 2 × 5/100)
⇒ $5610 = P (1 + 10/100)
⇒ $5610 = P (100 + 10/100)
⇒ $5610 = P × 110/100
⇒ P × 110/100 = $5610
⇒ P = 5610/110/100
⇒ P = 5610 × 100/110
⇒ P = 5610 × 100/110
⇒ P = 561000/110
⇒ P = $5100
Thus, the sum borrowed (P) = $5100 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 5610, then the Principal = 100/110 × 5610
= 100 × 5610/110
= 561000/110
= 5100
Thus, Principal = $5100
Thus, the sum borrowed = $5100 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.
(2) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?
(4) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.
(5) How much loan did Emily borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8437.5 to clear it?
(6) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.
(7) What amount does David have to pay after 6 years if he takes a loan of $3400 at 8% simple interest?
(8) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 7 years.
(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 2% simple interest?
(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.