Question:
If Kimberly paid $5394 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4650
Solution And Explanation
Solution
Given,
Amount (A) = $5394
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
$5394 = P (1 + 4% × 4)
⇒ $5394 = P (1 + 4/100 × 4)
⇒ $5394 = P (1 + 4 × 4/100)
⇒ $5394 = P (1 + 16/100)
⇒ $5394 = P (100 + 16/100)
⇒ $5394 = P × 116/100
⇒ P × 116/100 = $5394
⇒ P = 5394/116/100
⇒ P = 5394 × 100/116
⇒ P = 5394 × 100/116
⇒ P = 539400/116
⇒ P = $4650
Thus, the sum borrowed (P) = $4650 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 5394, then the Principal = 100/116 × 5394
= 100 × 5394/116
= 539400/116
= 4650
Thus, Principal = $4650
Thus, the sum borrowed = $4650 Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 3 years.
(2) If Kenneth paid $5800 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 8% simple interest?
(4) What amount does David have to pay after 6 years if he takes a loan of $3400 at 4% simple interest?
(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 3 years.
(6) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.
(7) How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?
(8) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?
(9) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.
(10) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 8% simple interest?