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) How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?
(2) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 3% simple interest?
(3) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 3 years.
(5) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 4 years.
(6) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 4 years.
(8) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(9) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?
(10) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?