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) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.
(2) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.
(3) How much loan did William borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6600 to clear it?
(4) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.
(6) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 5% simple interest?
(7) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?
(8) Richard had to pay $4140 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?
(10) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.