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) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(2) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12127 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.
(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 8 years.
(5) What amount does William have to pay after 6 years if he takes a loan of $3500 at 8% simple interest?
(6) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(7) How much loan did Lisa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7260 to clear it?
(8) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.
(9) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 4 years.