Question:
If Sandra paid $5162 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4450
Solution And Explanation
Solution
Given,
Amount (A) = $5162
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
$5162 = P (1 + 4% × 4)
⇒ $5162 = P (1 + 4/100 × 4)
⇒ $5162 = P (1 + 4 × 4/100)
⇒ $5162 = P (1 + 16/100)
⇒ $5162 = P (100 + 16/100)
⇒ $5162 = P × 116/100
⇒ P × 116/100 = $5162
⇒ P = 5162/116/100
⇒ P = 5162 × 100/116
⇒ P = 5162 × 100/116
⇒ P = 516200/116
⇒ P = $4450
Thus, the sum borrowed (P) = $4450 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 5162, then the Principal = 100/116 × 5162
= 100 × 5162/116
= 516200/116
= 4450
Thus, Principal = $4450
Thus, the sum borrowed = $4450 Answer
Similar Questions
(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.
(2) If Christopher paid $4800 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 7% simple interest?
(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.
(5) Elizabeth had to pay $3967.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) How much loan did Ashley borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7532.5 to clear it?
(7) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.
(8) Daniel had to pay $4715 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 9% simple interest?
(10) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.