Question:
If Donald paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4500
Solution And Explanation
Solution
Given,
Amount (A) = $5220
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
$5220 = P (1 + 4% × 4)
⇒ $5220 = P (1 + 4/100 × 4)
⇒ $5220 = P (1 + 4 × 4/100)
⇒ $5220 = P (1 + 16/100)
⇒ $5220 = P (100 + 16/100)
⇒ $5220 = P × 116/100
⇒ P × 116/100 = $5220
⇒ P = 5220/116/100
⇒ P = 5220 × 100/116
⇒ P = 5220 × 100/116
⇒ P = 522000/116
⇒ P = $4500
Thus, the sum borrowed (P) = $4500 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 5220, then the Principal = 100/116 × 5220
= 100 × 5220/116
= 522000/116
= 4500
Thus, Principal = $4500
Thus, the sum borrowed = $4500 Answer
Similar Questions
(1) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.
(2) How much loan did Ronald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9375 to clear it?
(3) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?
(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 8 years.
(5) How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?
(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 4 years.
(7) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 4 years.
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 7 years.
(9) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 10% simple interest?
(10) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.