Question:
How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?
Correct Answer
$7500
Solution And Explanation
Solution
Given,
Amount (A) = $8625
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
$8625 = P (1 + 3% × 5)
⇒ $8625 = P (1 + 3/100 × 5)
⇒ $8625 = P (1 + 3 × 5/100)
⇒ $8625 = P (1 + 15/100)
⇒ $8625 = P (100 + 15/100)
⇒ $8625 = P × 115/100
⇒ P × 115/100 = $8625
⇒ P = 8625/115/100
⇒ P = 8625 × 100/115
⇒ P = 8625 × 100/115
⇒ P = 862500/115
⇒ P = $7500
Thus, the sum borrowed (P) = $7500 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 8625, then the Principal = 100/115 × 8625
= 100 × 8625/115
= 862500/115
= 7500
Thus, Principal = $7500
Thus, the sum borrowed = $7500 Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 7 years.
(3) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.
(4) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
(5) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 4 years.
(7) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(8) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 10% simple interest?
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 4 years.
(10) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 9% simple interest?