Question:
How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?
Correct Answer
$6800
Solution And Explanation
Solution
Given,
Amount (A) = $7480
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
$7480 = P (1 + 2% × 5)
⇒ $7480 = P (1 + 2/100 × 5)
⇒ $7480 = P (1 + 2 × 5/100)
⇒ $7480 = P (1 + 10/100)
⇒ $7480 = P (100 + 10/100)
⇒ $7480 = P × 110/100
⇒ P × 110/100 = $7480
⇒ P = 7480/110/100
⇒ P = 7480 × 100/110
⇒ P = 7480 × 100/110
⇒ P = 748000/110
⇒ P = $6800
Thus, the sum borrowed (P) = $6800 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 7480, then the Principal = 100/110 × 7480
= 100 × 7480/110
= 748000/110
= 6800
Thus, Principal = $6800
Thus, the sum borrowed = $6800 Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(2) How much loan did Donna borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8220 to clear it?
(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 8 years.
(4) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 3% simple interest?
(5) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 7 years.
(7) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?
(8) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?
(9) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?
(10) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 4% simple interest?