Question:
If Anthony paid $4988 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4300
Solution And Explanation
Solution
Given,
Amount (A) = $4988
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
$4988 = P (1 + 4% × 4)
⇒ $4988 = P (1 + 4/100 × 4)
⇒ $4988 = P (1 + 4 × 4/100)
⇒ $4988 = P (1 + 16/100)
⇒ $4988 = P (100 + 16/100)
⇒ $4988 = P × 116/100
⇒ P × 116/100 = $4988
⇒ P = 4988/116/100
⇒ P = 4988 × 100/116
⇒ P = 4988 × 100/116
⇒ P = 498800/116
⇒ 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 = 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 4988, then the Principal = 100/116 × 4988
= 100 × 4988/116
= 498800/116
= 4300
Thus, Principal = $4300
Thus, the sum borrowed = $4300 Answer
Similar Questions
(1) Calculate the amount due if Charles borrowed a sum of $3900 at 4% simple interest for 4 years.
(2) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 8% simple interest?
(3) In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?
(4) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
(5) Kimberly had to pay $5208 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 10% simple interest?
(7) Andrew had to pay $5232 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) What amount does James have to pay after 6 years if he takes a loan of $3000 at 8% simple interest?
(9) In how much time a principal of $3000 will amount to $3360 at a simple interest of 3% per annum?
(10) Linda had to pay $3551 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.