Question:
How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?
Correct Answer
$6300
Solution And Explanation
Solution
Given,
Amount (A) = $6930
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
$6930 = P (1 + 2% × 5)
⇒ $6930 = P (1 + 2/100 × 5)
⇒ $6930 = P (1 + 2 × 5/100)
⇒ $6930 = P (1 + 10/100)
⇒ $6930 = P (100 + 10/100)
⇒ $6930 = P × 110/100
⇒ P × 110/100 = $6930
⇒ P = 6930/110/100
⇒ P = 6930 × 100/110
⇒ P = 6930 × 100/110
⇒ P = 693000/110
⇒ P = $6300
Thus, the sum borrowed (P) = $6300 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 6930, then the Principal = 100/110 × 6930
= 100 × 6930/110
= 693000/110
= 6300
Thus, Principal = $6300
Thus, the sum borrowed = $6300 Answer
Similar Questions
(1) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 5% simple interest?
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 7 years.
(3) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 7 years.
(6) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(7) How much loan did Edward borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9120 to clear it?
(8) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 8% simple interest?
(9) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 8 years.