Question:
How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?
Correct Answer
$7000
Solution And Explanation
Solution
Given,
Amount (A) = $8400
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
$8400 = P (1 + 4% × 5)
⇒ $8400 = P (1 + 4/100 × 5)
⇒ $8400 = P (1 + 4 × 5/100)
⇒ $8400 = P (1 + 20/100)
⇒ $8400 = P (100 + 20/100)
⇒ $8400 = P × 120/100
⇒ P × 120/100 = $8400
⇒ P = 8400/120/100
⇒ P = 8400 × 100/120
⇒ P = 8400 × 100/120
⇒ P = 840000/120
⇒ P = $7000
Thus, the sum borrowed (P) = $7000 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 8400, then the Principal = 100/120 × 8400
= 100 × 8400/120
= 840000/120
= 7000
Thus, Principal = $7000
Thus, the sum borrowed = $7000 Answer
Similar Questions
(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 3 years.
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 7 years.
(3) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8797.5 to clear it?
(4) In how much time a principal of $3000 will amount to $3300 at a simple interest of 5% per annum?
(5) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
(6) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(7) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 10% simple interest?
(8) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.
(9) How much loan did Donna borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8562.5 to clear it?
(10) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.