Question:
If Daniel paid $4756 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4100
Solution And Explanation
Solution
Given,
Amount (A) = $4756
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
$4756 = P (1 + 4% × 4)
⇒ $4756 = P (1 + 4/100 × 4)
⇒ $4756 = P (1 + 4 × 4/100)
⇒ $4756 = P (1 + 16/100)
⇒ $4756 = P (100 + 16/100)
⇒ $4756 = P × 116/100
⇒ P × 116/100 = $4756
⇒ P = 4756/116/100
⇒ P = 4756 × 100/116
⇒ P = 4756 × 100/116
⇒ P = 475600/116
⇒ P = $4100
Thus, the sum borrowed (P) = $4100 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 4756, then the Principal = 100/116 × 4756
= 100 × 4756/116
= 475600/116
= 4100
Thus, Principal = $4100
Thus, the sum borrowed = $4100 Answer
Similar Questions
(1) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.
(3) How much loan did George borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8760 to clear it?
(4) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 8 years.
(5) Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 2% simple interest?
(7) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 3% simple interest?
(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 8 years.
(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 7 years.
(10) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 4% simple interest?