Question:
How much loan did Robert borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5865 to clear it?
Correct Answer
$5100
Solution And Explanation
Solution
Given,
Amount (A) = $5865
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
$5865 = P (1 + 3% × 5)
⇒ $5865 = P (1 + 3/100 × 5)
⇒ $5865 = P (1 + 3 × 5/100)
⇒ $5865 = P (1 + 15/100)
⇒ $5865 = P (100 + 15/100)
⇒ $5865 = P × 115/100
⇒ P × 115/100 = $5865
⇒ P = 5865/115/100
⇒ P = 5865 × 100/115
⇒ P = 5865 × 100/115
⇒ P = 586500/115
⇒ P = $5100
Thus, the sum borrowed (P) = $5100 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 5865, then the Principal = 100/115 × 5865
= 100 × 5865/115
= 586500/115
= 5100
Thus, Principal = $5100
Thus, the sum borrowed = $5100 Answer
Similar Questions
(1) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 8 years.
(3) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 7 years.
(5) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 4 years.
(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.
(7) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7208 to clear the loan, then find the time period of the loan.
(8) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 4 years.
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 8 years.