Question:
How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?
Correct Answer
$6450
Solution And Explanation
Solution
Given,
Amount (A) = $7417.5
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
$7417.5 = P (1 + 3% × 5)
⇒ $7417.5 = P (1 + 3/100 × 5)
⇒ $7417.5 = P (1 + 3 × 5/100)
⇒ $7417.5 = P (1 + 15/100)
⇒ $7417.5 = P (100 + 15/100)
⇒ $7417.5 = P × 115/100
⇒ P × 115/100 = $7417.5
⇒ P = 7417.5/115/100
⇒ P = 7417.5 × 100/115
⇒ P = 7417.5 × 100/115
⇒ P = 741750/115
⇒ P = $6450
Thus, the sum borrowed (P) = $6450 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 7417.5, then the Principal = 100/115 × 7417.5
= 100 × 7417.5/115
= 741750/115
= 6450
Thus, Principal = $6450
Thus, the sum borrowed = $6450 Answer
Similar Questions
(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 4 years.
(2) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11403 to clear the loan, then find the time period of the loan.
(3) If Michelle paid $5940 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 3 years.
(5) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(6) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(7) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 8 years.
(9) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 3 years.