Question:
( 1 of 10 ) Karen had to pay $4305.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(A) 753
(B) 376
(C) 751
(D) 752
You selected
$3229.13
Correct Answer
$3950
Solution And Explanation
Solution
Given,
Amount (A) = $4305.5
Rate of Simple Interest (R) = 3%
Time (T) = 3 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
$4305.5 = P (1 + 3% × 3)
⇒ $4305.5 = P (1 + 3/100 × 3)
⇒ $4305.5 = P (1 + 3 × 3/100)
⇒ $4305.5 = P (1 + 9/100)
⇒ $4305.5 = P (100 + 9/100)
⇒ $4305.5 = P × 109/100
⇒ P × 109/100 = $4305.5
⇒ P = 4305.5/109/100
⇒ P = 4305.5 × 100/109
⇒ P = 4305.5 × 100/109
⇒ P = 430550/109
⇒ 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
Calculation of the Amount
Since, in the question, time = 3 years
So, we need to calculate the simple interest for the given time period, which is 3 years
Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year
= 3 × 3 = 9
Thus, simple interest for 3 years = 9
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 9 = 109
Calculation of the Principal
Now,
∵ If the Amount is 109, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/109
∴ If the Amount is 4305.5, then the Principal = 100/109 × 4305.5
= 100 × 4305.5/109
= 430550/109
= 3950
Thus, Principal = $3950
Thus, the sum borrowed = $3950 Answer
Similar Questions
(1) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 8% simple interest?
(2) How much loan did Michelle borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7645 to clear it?
(3) Thomas had to pay $4028 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) Paul had to pay $5123 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.
(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 7 years.
(8) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(9) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 4% simple interest?
(10) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.