Question:
If Anthony paid $4816 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$4300
Solution And Explanation
Solution
Given,
Amount (A) = $4816
Rate of Simple Interest (R) = 3%
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
$4816 = P (1 + 3% × 4)
⇒ $4816 = P (1 + 3/100 × 4)
⇒ $4816 = P (1 + 3 × 4/100)
⇒ $4816 = P (1 + 12/100)
⇒ $4816 = P (100 + 12/100)
⇒ $4816 = P × 112/100
⇒ P × 112/100 = $4816
⇒ P = 4816/112/100
⇒ P = 4816 × 100/112
⇒ P = 4816 × 100/112
⇒ P = 481600/112
⇒ 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 12
Thus, simple interest for 4 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 4816, then the Principal = 100/112 × 4816
= 100 × 4816/112
= 481600/112
= 4300
Thus, Principal = $4300
Thus, the sum borrowed = $4300 Answer
Similar Questions
(1) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 8 years.
(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 8 years.
(3) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(4) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.
(5) How much loan did Deborah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8567.5 to clear it?
(6) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.
(8) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 6% simple interest?
(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.
(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 3 years.