Question:
How much loan did Michelle borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7992.5 to clear it?
Correct Answer
$6950
Solution And Explanation
Solution
Given,
Amount (A) = $7992.5
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
$7992.5 = P (1 + 3% × 5)
⇒ $7992.5 = P (1 + 3/100 × 5)
⇒ $7992.5 = P (1 + 3 × 5/100)
⇒ $7992.5 = P (1 + 15/100)
⇒ $7992.5 = P (100 + 15/100)
⇒ $7992.5 = P × 115/100
⇒ P × 115/100 = $7992.5
⇒ P = 7992.5/115/100
⇒ P = 7992.5 × 100/115
⇒ P = 7992.5 × 100/115
⇒ P = 799250/115
⇒ P = $6950
Thus, the sum borrowed (P) = $6950 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 7992.5, then the Principal = 100/115 × 7992.5
= 100 × 7992.5/115
= 799250/115
= 6950
Thus, Principal = $6950
Thus, the sum borrowed = $6950 Answer
Similar Questions
(1) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 4 years.
(2) How much loan did Brian borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9000 to clear it?
(3) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.
(4) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.
(5) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.
(6) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(7) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.
(8) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 4 years.
(10) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 6% simple interest.