Question:
How much loan did Richard borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7000 to clear it?
Correct Answer
$5600
Solution And Explanation
Solution
Given,
Amount (A) = $7000
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
$7000 = P (1 + 5% × 5)
⇒ $7000 = P (1 + 5/100 × 5)
⇒ $7000 = P (1 + 5 × 5/100)
⇒ $7000 = P (1 + 25/100)
⇒ $7000 = P (100 + 25/100)
⇒ $7000 = P × 125/100
⇒ P × 125/100 = $7000
⇒ P = 7000/125/100
⇒ P = 7000 × 100/125
⇒ P = 7000 × 100/125
⇒ P = 700000/125
⇒ P = $5600
Thus, the sum borrowed (P) = $5600 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 7000, then the Principal = 100/125 × 7000
= 100 × 7000/125
= 700000/125
= 5600
Thus, Principal = $5600
Thus, the sum borrowed = $5600 Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 3 years.
(3) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 7% simple interest?
(4) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 9% simple interest?
(5) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?
(6) In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?
(7) How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?
(8) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 3 years.
(10) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 5% simple interest?