Question:
How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?
Correct Answer
$7700
Solution And Explanation
Solution
Given,
Amount (A) = $8470
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
$8470 = P (1 + 2% × 5)
⇒ $8470 = P (1 + 2/100 × 5)
⇒ $8470 = P (1 + 2 × 5/100)
⇒ $8470 = P (1 + 10/100)
⇒ $8470 = P (100 + 10/100)
⇒ $8470 = P × 110/100
⇒ P × 110/100 = $8470
⇒ P = 8470/110/100
⇒ P = 8470 × 100/110
⇒ P = 8470 × 100/110
⇒ P = 847000/110
⇒ P = $7700
Thus, the sum borrowed (P) = $7700 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 8470, then the Principal = 100/110 × 8470
= 100 × 8470/110
= 847000/110
= 7700
Thus, Principal = $7700
Thus, the sum borrowed = $7700 Answer
Similar Questions
(1) What amount will be due after 2 years if James borrowed a sum of $3000 at a 5% simple interest?
(2) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9348 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.
(4) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.
(6) 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?
(7) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
(9) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 7% simple interest?
(10) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.