Question:
How much loan did Jessica borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6900 to clear it?
Correct Answer
$5750
Solution And Explanation
Solution
Given,
Amount (A) = $6900
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
$6900 = P (1 + 4% × 5)
⇒ $6900 = P (1 + 4/100 × 5)
⇒ $6900 = P (1 + 4 × 5/100)
⇒ $6900 = P (1 + 20/100)
⇒ $6900 = P (100 + 20/100)
⇒ $6900 = P × 120/100
⇒ P × 120/100 = $6900
⇒ P = 6900/120/100
⇒ P = 6900 × 100/120
⇒ P = 6900 × 100/120
⇒ P = 690000/120
⇒ P = $5750
Thus, the sum borrowed (P) = $5750 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 6900, then the Principal = 100/120 × 6900
= 100 × 6900/120
= 690000/120
= 5750
Thus, Principal = $5750
Thus, the sum borrowed = $5750 Answer
Similar Questions
(1) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 3% simple interest?
(2) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.
(4) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 5% simple interest?
(5) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.
(6) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.
(7) How much loan did Barbara borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6937.5 to clear it?
(8) If Elizabeth paid $3726 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) What amount does John have to pay after 5 years if he takes a loan of $3200 at 3% simple interest?
(10) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?