Question:
If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4750
Solution And Explanation
Solution
Given,
Amount (A) = $5700
Rate of Simple Interest (R) = 5%
Time (T) = 4 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
$5700 = P (1 + 5% × 4)
⇒ $5700 = P (1 + 5/100 × 4)
⇒ $5700 = P (1 + 5 × 4/100)
⇒ $5700 = P (1 + 20/100)
⇒ $5700 = P (100 + 20/100)
⇒ $5700 = P × 120/100
⇒ P × 120/100 = $5700
⇒ P = 5700/120/100
⇒ P = 5700 × 100/120
⇒ P = 5700 × 100/120
⇒ P = 570000/120
⇒ P = $4750
Thus, the sum borrowed (P) = $4750 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 = 4 years
So, we need to calculate the simple interest for the given time period, which is 4 years
Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year
= 4 × 5 = 20
Thus, simple interest for 4 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 5700, then the Principal = 100/120 × 5700
= 100 × 5700/120
= 570000/120
= 4750
Thus, Principal = $4750
Thus, the sum borrowed = $4750 Answer
Similar Questions
(1) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 3% simple interest?
(2) If John paid $3456 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) How much loan did Daniel borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7320 to clear it?
(4) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6528 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.
(6) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 5% simple interest.
(7) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 6% simple interest?
(8) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8296 to clear the loan, then find the time period of the loan.
(9) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 3 years.