Question:
If Emily paid $5510 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4750
Solution And Explanation
Solution
Given,
Amount (A) = $5510
Rate of Simple Interest (R) = 4%
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
$5510 = P (1 + 4% × 4)
⇒ $5510 = P (1 + 4/100 × 4)
⇒ $5510 = P (1 + 4 × 4/100)
⇒ $5510 = P (1 + 16/100)
⇒ $5510 = P (100 + 16/100)
⇒ $5510 = P × 116/100
⇒ P × 116/100 = $5510
⇒ P = 5510/116/100
⇒ P = 5510 × 100/116
⇒ P = 5510 × 100/116
⇒ P = 551000/116
⇒ 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 = 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 = 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 × 4 = 16
Thus, simple interest for 4 years = 16
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 16 = 116
Calculation of the Principal
Now,
∵ If the Amount is 116, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/116
∴ If the Amount is 5510, then the Principal = 100/116 × 5510
= 100 × 5510/116
= 551000/116
= 4750
Thus, Principal = $4750
Thus, the sum borrowed = $4750 Answer
Similar Questions
(1) If Jessica paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.
(3) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 4 years.
(5) If William paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 7 years.
(7) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8642 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 3 years.
(9) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 4 years.
(10) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 7% simple interest?