Question:
How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?
Correct Answer
$6850
Solution And Explanation
Solution
Given,
Amount (A) = $7877.5
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
$7877.5 = P (1 + 3% × 5)
⇒ $7877.5 = P (1 + 3/100 × 5)
⇒ $7877.5 = P (1 + 3 × 5/100)
⇒ $7877.5 = P (1 + 15/100)
⇒ $7877.5 = P (100 + 15/100)
⇒ $7877.5 = P × 115/100
⇒ P × 115/100 = $7877.5
⇒ P = 7877.5/115/100
⇒ P = 7877.5 × 100/115
⇒ P = 7877.5 × 100/115
⇒ P = 787750/115
⇒ P = $6850
Thus, the sum borrowed (P) = $6850 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 7877.5, then the Principal = 100/115 × 7877.5
= 100 × 7877.5/115
= 787750/115
= 6850
Thus, Principal = $6850
Thus, the sum borrowed = $6850 Answer
Similar Questions
(1) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 3 years.
(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 7 years.
(3) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?
(4) In how much time a principal of $3150 will amount to $3276 at a simple interest of 2% per annum?
(5) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 3 years.
(6) If Nancy paid $4814 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7700 to clear it?
(8) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(9) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 10% simple interest?