Question:
How much loan did William borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6600 to clear it?
Correct Answer
$5500
Solution And Explanation
Solution
Given,
Amount (A) = $6600
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
$6600 = P (1 + 4% × 5)
⇒ $6600 = P (1 + 4/100 × 5)
⇒ $6600 = P (1 + 4 × 5/100)
⇒ $6600 = P (1 + 20/100)
⇒ $6600 = P (100 + 20/100)
⇒ $6600 = P × 120/100
⇒ P × 120/100 = $6600
⇒ P = 6600/120/100
⇒ P = 6600 × 100/120
⇒ P = 6600 × 100/120
⇒ P = 660000/120
⇒ P = $5500
Thus, the sum borrowed (P) = $5500 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 6600, then the Principal = 100/120 × 6600
= 100 × 6600/120
= 660000/120
= 5500
Thus, Principal = $5500
Thus, the sum borrowed = $5500 Answer
Similar Questions
(1) 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.
(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 7 years.
(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 8 years.
(4) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 5% simple interest?
(5) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
(6) How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?
(7) How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?
(8) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.
(9) How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?
(10) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.