Question:
If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3950
Solution And Explanation
Solution
Given,
Amount (A) = $4582
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
$4582 = P (1 + 4% × 4)
⇒ $4582 = P (1 + 4/100 × 4)
⇒ $4582 = P (1 + 4 × 4/100)
⇒ $4582 = P (1 + 16/100)
⇒ $4582 = P (100 + 16/100)
⇒ $4582 = P × 116/100
⇒ P × 116/100 = $4582
⇒ P = 4582/116/100
⇒ P = 4582 × 100/116
⇒ P = 4582 × 100/116
⇒ P = 458200/116
⇒ P = $3950
Thus, the sum borrowed (P) = $3950 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 4582, then the Principal = 100/116 × 4582
= 100 × 4582/116
= 458200/116
= 3950
Thus, Principal = $3950
Thus, the sum borrowed = $3950 Answer
Similar Questions
(1) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 8% simple interest?
(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?
(3) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.
(5) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 10% simple interest?
(6) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?
(7) What amount does David have to pay after 5 years if he takes a loan of $3400 at 2% simple interest?
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.
(9) Michelle had to pay $5247 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.