Question:
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?
Correct Answer
$6000
Solution And Explanation
Solution
Given,
Amount (A) = $7200
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
$7200 = P (1 + 4% × 5)
⇒ $7200 = P (1 + 4/100 × 5)
⇒ $7200 = P (1 + 4 × 5/100)
⇒ $7200 = P (1 + 20/100)
⇒ $7200 = P (100 + 20/100)
⇒ $7200 = P × 120/100
⇒ P × 120/100 = $7200
⇒ P = 7200/120/100
⇒ P = 7200 × 100/120
⇒ P = 7200 × 100/120
⇒ P = 720000/120
⇒ P = $6000
Thus, the sum borrowed (P) = $6000 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 7200, then the Principal = 100/120 × 7200
= 100 × 7200/120
= 720000/120
= 6000
Thus, Principal = $6000
Thus, the sum borrowed = $6000 Answer
Similar Questions
(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 8 years.
(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 8 years.
(3) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.
(4) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.
(5) What amount does William have to pay after 6 years if he takes a loan of $3500 at 6% simple interest?
(6) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.
(7) In how much time a principal of $3100 will amount to $3410 at a simple interest of 5% per annum?
(8) If Richard borrowed $3600 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 7 years.
(10) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?