Question:
How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?
Correct Answer
$5150
Solution And Explanation
Solution
Given,
Amount (A) = $5922.5
Rate of Simple Interest (R) = 3%
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
$5922.5 = P (1 + 3% × 5)
⇒ $5922.5 = P (1 + 3/100 × 5)
⇒ $5922.5 = P (1 + 3 × 5/100)
⇒ $5922.5 = P (1 + 15/100)
⇒ $5922.5 = P (100 + 15/100)
⇒ $5922.5 = P × 115/100
⇒ P × 115/100 = $5922.5
⇒ P = 5922.5/115/100
⇒ P = 5922.5 × 100/115
⇒ P = 5922.5 × 100/115
⇒ P = 592250/115
⇒ P = $5150
Thus, the sum borrowed (P) = $5150 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 5922.5, then the Principal = 100/115 × 5922.5
= 100 × 5922.5/115
= 592250/115
= 5150
Thus, Principal = $5150
Thus, the sum borrowed = $5150 Answer
Similar Questions
(1) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 3 years.
(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 8 years.
(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.
(4) How much loan did Amanda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8937.5 to clear it?
(5) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.
(7) How much loan did Richard borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6160 to clear it?
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 7 years.
(9) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?
(10) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 7 years.