Question:
How much loan did Donald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7150 to clear it?
Correct Answer
$6500
Solution And Explanation
Solution
Given,
Amount (A) = $7150
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
$7150 = P (1 + 2% × 5)
⇒ $7150 = P (1 + 2/100 × 5)
⇒ $7150 = P (1 + 2 × 5/100)
⇒ $7150 = P (1 + 10/100)
⇒ $7150 = P (100 + 10/100)
⇒ $7150 = P × 110/100
⇒ P × 110/100 = $7150
⇒ P = 7150/110/100
⇒ P = 7150 × 100/110
⇒ P = 7150 × 100/110
⇒ P = 715000/110
⇒ P = $6500
Thus, the sum borrowed (P) = $6500 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 7150, then the Principal = 100/110 × 7150
= 100 × 7150/110
= 715000/110
= 6500
Thus, Principal = $6500
Thus, the sum borrowed = $6500 Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8046 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 8 years.
(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 4 years.
(5) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?
(6) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
(7) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 3 years.
(8) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 10% simple interest?
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 4 years.
(10) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.