Question:
How much loan did Thomas borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6960 to clear it?
Correct Answer
$5800
Solution And Explanation
Solution
Given,
Amount (A) = $6960
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
$6960 = P (1 + 4% × 5)
⇒ $6960 = P (1 + 4/100 × 5)
⇒ $6960 = P (1 + 4 × 5/100)
⇒ $6960 = P (1 + 20/100)
⇒ $6960 = P (100 + 20/100)
⇒ $6960 = P × 120/100
⇒ P × 120/100 = $6960
⇒ P = 6960/120/100
⇒ P = 6960 × 100/120
⇒ P = 6960 × 100/120
⇒ P = 696000/120
⇒ P = $5800
Thus, the sum borrowed (P) = $5800 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 6960, then the Principal = 100/120 × 6960
= 100 × 6960/120
= 696000/120
= 5800
Thus, Principal = $5800
Thus, the sum borrowed = $5800 Answer
Similar Questions
(1) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?
(2) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?
(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 3 years.
(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 8 years.
(5) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.
(6) If Paul paid $5640 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 3% simple interest?
(8) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
(9) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
(10) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 4 years.