Question:
How much loan did Melissa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8452.5 to clear it?
Correct Answer
$7350
Solution And Explanation
Solution
Given,
Amount (A) = $8452.5
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
$8452.5 = P (1 + 3% × 5)
⇒ $8452.5 = P (1 + 3/100 × 5)
⇒ $8452.5 = P (1 + 3 × 5/100)
⇒ $8452.5 = P (1 + 15/100)
⇒ $8452.5 = P (100 + 15/100)
⇒ $8452.5 = P × 115/100
⇒ P × 115/100 = $8452.5
⇒ P = 8452.5/115/100
⇒ P = 8452.5 × 100/115
⇒ P = 8452.5 × 100/115
⇒ P = 845250/115
⇒ P = $7350
Thus, the sum borrowed (P) = $7350 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 8452.5, then the Principal = 100/115 × 8452.5
= 100 × 8452.5/115
= 845250/115
= 7350
Thus, Principal = $7350
Thus, the sum borrowed = $7350 Answer
Similar Questions
(1) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 3 years.
(2) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.
(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.
(4) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if David borrowed a sum of $3200 at a 9% simple interest?
(6) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.
(7) If Linda paid $3618 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.
(9) How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?
(10) What amount will be due after 2 years if William borrowed a sum of $3250 at a 9% simple interest?