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) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?
(2) If Barbara paid $3976 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 7 years.
(4) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.
(5) If Kimberly paid $5022 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 7 years.
(7) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 4 years.
(8) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 3 years.
(9) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 3 years.