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) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8507 to clear the loan, then find the time period of the loan.
(2) How much loan did Jason borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9625 to clear it?
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.
(4) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 3 years.
(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 3 years.
(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 8 years.
(8) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if James borrowed a sum of $3000 at a 10% simple interest?
(10) Jennifer had to pay $3542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.