Question:
How much loan did George borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8030 to clear it?
Correct Answer
$7300
Solution And Explanation
Solution
Given,
Amount (A) = $8030
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
$8030 = P (1 + 2% × 5)
⇒ $8030 = P (1 + 2/100 × 5)
⇒ $8030 = P (1 + 2 × 5/100)
⇒ $8030 = P (1 + 10/100)
⇒ $8030 = P (100 + 10/100)
⇒ $8030 = P × 110/100
⇒ P × 110/100 = $8030
⇒ P = 8030/110/100
⇒ P = 8030 × 100/110
⇒ P = 8030 × 100/110
⇒ P = 803000/110
⇒ P = $7300
Thus, the sum borrowed (P) = $7300 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 8030, then the Principal = 100/110 × 8030
= 100 × 8030/110
= 803000/110
= 7300
Thus, Principal = $7300
Thus, the sum borrowed = $7300 Answer
Similar Questions
(1) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 8 years.
(3) What amount will be due after 2 years if David borrowed a sum of $3200 at a 8% simple interest?
(4) How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 8 years.
(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 3 years.
(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.
(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?
(9) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.
(10) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.