Question:
How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?
Correct Answer
$6700
Solution And Explanation
Solution
Given,
Amount (A) = $7370
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
$7370 = P (1 + 2% × 5)
⇒ $7370 = P (1 + 2/100 × 5)
⇒ $7370 = P (1 + 2 × 5/100)
⇒ $7370 = P (1 + 10/100)
⇒ $7370 = P (100 + 10/100)
⇒ $7370 = P × 110/100
⇒ P × 110/100 = $7370
⇒ P = 7370/110/100
⇒ P = 7370 × 100/110
⇒ P = 7370 × 100/110
⇒ P = 737000/110
⇒ P = $6700
Thus, the sum borrowed (P) = $6700 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 7370, then the Principal = 100/110 × 7370
= 100 × 7370/110
= 737000/110
= 6700
Thus, Principal = $6700
Thus, the sum borrowed = $6700 Answer
Similar Questions
(1) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(2) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 4 years.
(3) How much loan did Melissa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8820 to clear it?
(4) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 8 years.
(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 3 years.
(7) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 6% simple interest?
(8) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.
(9) Emily had to pay $5462.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?