Question:
How much loan did Ronald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8250 to clear it?
Correct Answer
$7500
Solution And Explanation
Solution
Given,
Amount (A) = $8250
Rate of Simple Interest (R) = 2%
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
$8250 = P (1 + 2% × 5)
⇒ $8250 = P (1 + 2/100 × 5)
⇒ $8250 = P (1 + 2 × 5/100)
⇒ $8250 = P (1 + 10/100)
⇒ $8250 = P (100 + 10/100)
⇒ $8250 = P × 110/100
⇒ P × 110/100 = $8250
⇒ P = 8250/110/100
⇒ P = 8250 × 100/110
⇒ P = 8250 × 100/110
⇒ P = 825000/110
⇒ 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 8250, then the Principal = 100/110 × 8250
= 100 × 8250/110
= 825000/110
= 7500
Thus, Principal = $7500
Thus, the sum borrowed = $7500 Answer
Similar Questions
(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 8 years.
(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 3 years.
(3) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?
(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?
(5) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(6) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7344 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 3 years.
(9) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 3 years.
(10) How much loan did Christopher borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7500 to clear it?