Question:
If Anthony paid $4644 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4300
Solution And Explanation
Solution
Given,
Amount (A) = $4644
Rate of Simple Interest (R) = 2%
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
$4644 = P (1 + 2% × 4)
⇒ $4644 = P (1 + 2/100 × 4)
⇒ $4644 = P (1 + 2 × 4/100)
⇒ $4644 = P (1 + 8/100)
⇒ $4644 = P (100 + 8/100)
⇒ $4644 = P × 108/100
⇒ P × 108/100 = $4644
⇒ P = 4644/108/100
⇒ P = 4644 × 100/108
⇒ P = 4644 × 100/108
⇒ P = 464400/108
⇒ P = $4300
Thus, the sum borrowed (P) = $4300 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 4644, then the Principal = 100/108 × 4644
= 100 × 4644/108
= 464400/108
= 4300
Thus, Principal = $4300
Thus, the sum borrowed = $4300 Answer
Similar Questions
(1) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 8 years.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 4 years.
(4) What amount does James have to pay after 6 years if he takes a loan of $3000 at 2% simple interest?
(5) How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 7 years.
(7) Daniel had to pay $4469 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) If Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) Emily had to pay $5462.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.