Question:
How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?
Correct Answer
$7450
Solution And Explanation
Solution
Given,
Amount (A) = $8940
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
$8940 = P (1 + 4% × 5)
⇒ $8940 = P (1 + 4/100 × 5)
⇒ $8940 = P (1 + 4 × 5/100)
⇒ $8940 = P (1 + 20/100)
⇒ $8940 = P (100 + 20/100)
⇒ $8940 = P × 120/100
⇒ P × 120/100 = $8940
⇒ P = 8940/120/100
⇒ P = 8940 × 100/120
⇒ P = 8940 × 100/120
⇒ P = 894000/120
⇒ P = $7450
Thus, the sum borrowed (P) = $7450 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 8940, then the Principal = 100/120 × 8940
= 100 × 8940/120
= 894000/120
= 7450
Thus, Principal = $7450
Thus, the sum borrowed = $7450 Answer
Similar Questions
(1) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 7 years.
(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.
(3) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(4) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.
(5) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(6) How much loan did Kevin borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7810 to clear it?
(7) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
(8) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 10% simple interest?
(9) John had to pay $3392 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.