Question:
( 1 of 10 ) If Mark paid $5104 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(A) 4 47/50 Or, 247/50
(B) 8 47/50 Or, 447/50
(C) 4 141/50 Or, 341/50
(D) 4 94/50 Or, 294/50
You selected
$3828
Correct Answer
$4400
Solution And Explanation
Solution
Given,
Amount (A) = $5104
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
$5104 = P (1 + 4% × 4)
⇒ $5104 = P (1 + 4/100 × 4)
⇒ $5104 = P (1 + 4 × 4/100)
⇒ $5104 = P (1 + 16/100)
⇒ $5104 = P (100 + 16/100)
⇒ $5104 = P × 116/100
⇒ P × 116/100 = $5104
⇒ P = 5104/116/100
⇒ P = 5104 × 100/116
⇒ P = 5104 × 100/116
⇒ P = 510400/116
⇒ P = $4400
Thus, the sum borrowed (P) = $4400 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 5104, then the Principal = 100/116 × 5104
= 100 × 5104/116
= 510400/116
= 4400
Thus, Principal = $4400
Thus, the sum borrowed = $4400 Answer
Similar Questions
(1) What amount does John have to pay after 6 years if he takes a loan of $3200 at 5% simple interest?
(2) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?
(3) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.
(4) If Joshua paid $5684 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?
(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 7 years.
(7) How much loan did Daniel borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7015 to clear it?
(8) How much loan did Nancy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7072.5 to clear it?
(9) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 5% simple interest?
(10) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?