Question:
How much loan did Sharon borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9300 to clear it?
Correct Answer
$7750
Solution And Explanation
Solution
Given,
Amount (A) = $9300
Rate of Simple Interest (R) = 4%
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
$9300 = P (1 + 4% × 5)
⇒ $9300 = P (1 + 4/100 × 5)
⇒ $9300 = P (1 + 4 × 5/100)
⇒ $9300 = P (1 + 20/100)
⇒ $9300 = P (100 + 20/100)
⇒ $9300 = P × 120/100
⇒ P × 120/100 = $9300
⇒ P = 9300/120/100
⇒ P = 9300 × 100/120
⇒ P = 9300 × 100/120
⇒ P = 930000/120
⇒ P = $7750
Thus, the sum borrowed (P) = $7750 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 9300, then the Principal = 100/120 × 9300
= 100 × 9300/120
= 930000/120
= 7750
Thus, Principal = $7750
Thus, the sum borrowed = $7750 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.
(2) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
(3) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?
(4) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
(5) If Mark paid $5104 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.
(7) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 8 years.
(9) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 2% simple interest?
(10) If Patricia paid $3654 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.