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) 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?
(2) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.
(3) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 8% simple interest?
(4) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.
(5) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
(6) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(7) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 5% simple interest?
(8) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.
(9) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.