Question:
How much loan did Nancy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7072.5 to clear it?
Correct Answer
$6150
Solution And Explanation
Solution
Given,
Amount (A) = $7072.5
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
$7072.5 = P (1 + 3% × 5)
⇒ $7072.5 = P (1 + 3/100 × 5)
⇒ $7072.5 = P (1 + 3 × 5/100)
⇒ $7072.5 = P (1 + 15/100)
⇒ $7072.5 = P (100 + 15/100)
⇒ $7072.5 = P × 115/100
⇒ P × 115/100 = $7072.5
⇒ P = 7072.5/115/100
⇒ P = 7072.5 × 100/115
⇒ P = 7072.5 × 100/115
⇒ P = 707250/115
⇒ P = $6150
Thus, the sum borrowed (P) = $6150 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 7072.5, then the Principal = 100/115 × 7072.5
= 100 × 7072.5/115
= 707250/115
= 6150
Thus, Principal = $6150
Thus, the sum borrowed = $6150 Answer
Similar Questions
(1) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 3 years.
(2) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 7 years.
(4) What amount does James have to pay after 6 years if he takes a loan of $3000 at 3% simple interest?
(5) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.
(7) If Mark paid $5104 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 7 years.
(9) What amount will be due after 2 years if William borrowed a sum of $3250 at a 9% simple interest?
(10) What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?