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) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 2% simple interest?
(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 7 years.
(3) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 4 years.
(4) How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?
(5) Donna had to pay $5577.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 3 years.
(8) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
(9) How much loan did James borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6000 to clear it?
(10) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 6% simple interest?