Question:
How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?
Correct Answer
$7950
Solution And Explanation
Solution
Given,
Amount (A) = $9540
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
$9540 = P (1 + 4% × 5)
⇒ $9540 = P (1 + 4/100 × 5)
⇒ $9540 = P (1 + 4 × 5/100)
⇒ $9540 = P (1 + 20/100)
⇒ $9540 = P (100 + 20/100)
⇒ $9540 = P × 120/100
⇒ P × 120/100 = $9540
⇒ P = 9540/120/100
⇒ P = 9540 × 100/120
⇒ P = 9540 × 100/120
⇒ P = 954000/120
⇒ P = $7950
Thus, the sum borrowed (P) = $7950 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 9540, then the Principal = 100/120 × 9540
= 100 × 9540/120
= 954000/120
= 7950
Thus, Principal = $7950
Thus, the sum borrowed = $7950 Answer
Similar Questions
(1) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 3 years.
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.
(3) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 3% simple interest?
(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 7 years.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 7 years.
(6) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(7) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 7% simple interest?
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 8 years.
(9) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?
(10) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.