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) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?
(2) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.
(3) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 4% simple interest?
(4) In how much time a principal of $3150 will amount to $3937.5 at a simple interest of 5% per annum?
(5) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?
(6) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.
(8) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(9) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(10) How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?