Question:
How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?
Correct Answer
$8000
Solution And Explanation
Solution
Given,
Amount (A) = $9200
Rate of Simple Interest (R) = 3%
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
$9200 = P (1 + 3% × 5)
⇒ $9200 = P (1 + 3/100 × 5)
⇒ $9200 = P (1 + 3 × 5/100)
⇒ $9200 = P (1 + 15/100)
⇒ $9200 = P (100 + 15/100)
⇒ $9200 = P × 115/100
⇒ P × 115/100 = $9200
⇒ P = 9200/115/100
⇒ P = 9200 × 100/115
⇒ P = 9200 × 100/115
⇒ P = 920000/115
⇒ 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 9200, then the Principal = 100/115 × 9200
= 100 × 9200/115
= 920000/115
= 8000
Thus, Principal = $8000
Thus, the sum borrowed = $8000 Answer
Similar Questions
(1) If Paul paid $5076 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.
(3) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(4) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?
(5) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.
(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 8 years.
(7) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?
(8) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8750 to clear it?
(9) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.
(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 7 years.