Question:
How much loan did Edward borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8360 to clear it?
Correct Answer
$7600
Solution And Explanation
Solution
Given,
Amount (A) = $8360
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
$8360 = P (1 + 2% × 5)
⇒ $8360 = P (1 + 2/100 × 5)
⇒ $8360 = P (1 + 2 × 5/100)
⇒ $8360 = P (1 + 10/100)
⇒ $8360 = P (100 + 10/100)
⇒ $8360 = P × 110/100
⇒ P × 110/100 = $8360
⇒ P = 8360/110/100
⇒ P = 8360 × 100/110
⇒ P = 8360 × 100/110
⇒ P = 836000/110
⇒ P = $7600
Thus, the sum borrowed (P) = $7600 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 8360, then the Principal = 100/110 × 8360
= 100 × 8360/110
= 836000/110
= 7600
Thus, Principal = $7600
Thus, the sum borrowed = $7600 Answer
Similar Questions
(1) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 4 years.
(3) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?
(4) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 3 years.
(5) If Mary borrowed $3050 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(6) Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) If Joseph borrowed $3700 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(8) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 3 years.
(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 4 years.
(10) Joseph had to pay $4144 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.