Question:
( 1 of 10 ) If David paid $3944 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
$2958
Correct Answer
$3400
Solution And Explanation
Solution
Given,
Amount (A) = $3944
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
$3944 = P (1 + 4% × 4)
⇒ $3944 = P (1 + 4/100 × 4)
⇒ $3944 = P (1 + 4 × 4/100)
⇒ $3944 = P (1 + 16/100)
⇒ $3944 = P (100 + 16/100)
⇒ $3944 = P × 116/100
⇒ P × 116/100 = $3944
⇒ P = 3944/116/100
⇒ P = 3944 × 100/116
⇒ P = 3944 × 100/116
⇒ P = 394400/116
⇒ P = $3400
Thus, the sum borrowed (P) = $3400 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 3944, then the Principal = 100/116 × 3944
= 100 × 3944/116
= 394400/116
= 3400
Thus, Principal = $3400
Thus, the sum borrowed = $3400 Answer
Similar Questions
(1) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 6% simple interest?
(2) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
(3) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.
(4) How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?
(5) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?
(6) Sandra had to pay $4984 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 7 years.
(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 5% simple interest?
(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 8 years.
(10) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?