Question:
How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?
Correct Answer
$8000
Solution And Explanation
Solution
Given,
Amount (A) = $10000
Rate of Simple Interest (R) = 5%
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
$10000 = P (1 + 5% × 5)
⇒ $10000 = P (1 + 5/100 × 5)
⇒ $10000 = P (1 + 5 × 5/100)
⇒ $10000 = P (1 + 25/100)
⇒ $10000 = P (100 + 25/100)
⇒ $10000 = P × 125/100
⇒ P × 125/100 = $10000
⇒ P = 10000/125/100
⇒ P = 10000 × 100/125
⇒ P = 10000 × 100/125
⇒ P = 1000000/125
⇒ P = $8000
Thus, the sum borrowed (P) = $8000 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 10000, then the Principal = 100/125 × 10000
= 100 × 10000/125
= 1000000/125
= 8000
Thus, Principal = $8000
Thus, the sum borrowed = $8000 Answer
Similar Questions
(1) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
(2) Sandra had to pay $4984 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 7 years.
(5) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 7 years.
(7) If Christopher borrowed $4000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.
(9) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 3 years.
(10) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.