Question:
How much loan did Michael borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6095 to clear it?
Correct Answer
$5300
Solution And Explanation
Solution
Given,
Amount (A) = $6095
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
$6095 = P (1 + 3% × 5)
⇒ $6095 = P (1 + 3/100 × 5)
⇒ $6095 = P (1 + 3 × 5/100)
⇒ $6095 = P (1 + 15/100)
⇒ $6095 = P (100 + 15/100)
⇒ $6095 = P × 115/100
⇒ P × 115/100 = $6095
⇒ P = 6095/115/100
⇒ P = 6095 × 100/115
⇒ P = 6095 × 100/115
⇒ P = 609500/115
⇒ P = $5300
Thus, the sum borrowed (P) = $5300 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 6095, then the Principal = 100/115 × 6095
= 100 × 6095/115
= 609500/115
= 5300
Thus, Principal = $5300
Thus, the sum borrowed = $5300 Answer
Similar Questions
(1) What amount does John have to pay after 6 years if he takes a loan of $3200 at 8% simple interest?
(2) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 2% simple interest.
(3) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?
(4) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.
(5) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.
(6) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.
(7) If Ashley paid $5460 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.
(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 4% simple interest?
(10) How much loan did Daniel borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7320 to clear it?