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) If Thomas borrowed $3800 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(2) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(3) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 4% simple interest?
(4) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.
(5) If Susan paid $4088 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11222 to clear the loan, then find the time period of the loan.
(7) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 5% simple interest?
(8) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.
(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 7 years.