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 Karen borrowed a sum of $5950 at a rate of 3% simple interest.
(2) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.
(4) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?
(5) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?
(7) How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?
(8) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?
(9) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 3% simple interest?
(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.