Question:
How much loan did Steven borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7920 to clear it?
Correct Answer
$6600
Solution And Explanation
Solution
Given,
Amount (A) = $7920
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
$7920 = P (1 + 4% × 5)
⇒ $7920 = P (1 + 4/100 × 5)
⇒ $7920 = P (1 + 4 × 5/100)
⇒ $7920 = P (1 + 20/100)
⇒ $7920 = P (100 + 20/100)
⇒ $7920 = P × 120/100
⇒ P × 120/100 = $7920
⇒ P = 7920/120/100
⇒ P = 7920 × 100/120
⇒ P = 7920 × 100/120
⇒ P = 792000/120
⇒ P = $6600
Thus, the sum borrowed (P) = $6600 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 7920, then the Principal = 100/120 × 7920
= 100 × 7920/120
= 792000/120
= 6600
Thus, Principal = $6600
Thus, the sum borrowed = $6600 Answer
Similar Questions
(1) If Barbara paid $3976 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) What amount does David have to pay after 5 years if he takes a loan of $3400 at 7% simple interest?
(3) How much loan did Michelle borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8340 to clear it?
(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 3 years.
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 3 years.
(6) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?
(7) 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.
(8) How much loan did Melissa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8820 to clear it?
(9) What amount will be due after 2 years if James borrowed a sum of $3000 at a 8% simple interest?
(10) How much loan did Steven borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8250 to clear it?