Question:
How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9360 to clear it?
Correct Answer
$7800
Solution And Explanation
Solution
Given,
Amount (A) = $9360
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
$9360 = P (1 + 4% × 5)
⇒ $9360 = P (1 + 4/100 × 5)
⇒ $9360 = P (1 + 4 × 5/100)
⇒ $9360 = P (1 + 20/100)
⇒ $9360 = P (100 + 20/100)
⇒ $9360 = P × 120/100
⇒ P × 120/100 = $9360
⇒ P = 9360/120/100
⇒ P = 9360 × 100/120
⇒ P = 9360 × 100/120
⇒ P = 936000/120
⇒ P = $7800
Thus, the sum borrowed (P) = $7800 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 9360, then the Principal = 100/120 × 9360
= 100 × 9360/120
= 936000/120
= 7800
Thus, Principal = $7800
Thus, the sum borrowed = $7800 Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 4 years.
(2) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 7 years.
(4) In how much time a principal of $3000 will amount to $3240 at a simple interest of 4% per annum?
(5) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 3 years.
(6) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 9% simple interest?
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 8 years.
(8) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 9% simple interest?
(9) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 9% simple interest.
(10) If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.