Question:
Karen had to pay $4424 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
Correct Answer
$3950
Solution And Explanation
Solution
Given,
Amount (A) = $4424
Rate of Simple Interest (R) = 4%
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
$4424 = P (1 + 4% × 3)
⇒ $4424 = P (1 + 4/100 × 3)
⇒ $4424 = P (1 + 4 × 3/100)
⇒ $4424 = P (1 + 12/100)
⇒ $4424 = P (100 + 12/100)
⇒ $4424 = P × 112/100
⇒ P × 112/100 = $4424
⇒ P = 4424/112/100
⇒ P = 4424 × 100/112
⇒ P = 4424 × 100/112
⇒ P = 442400/112
⇒ 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 = 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 = 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 × 4 = 12
Thus, simple interest for 3 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 4424, then the Principal = 100/112 × 4424
= 100 × 4424/112
= 442400/112
= 3950
Thus, Principal = $3950
Thus, the sum borrowed = $3950 Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3200 will amount to $3488 at a simple interest of 3% per annum?
(3) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?
(4) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 10% simple interest?
(5) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 6% simple interest?
(6) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.
(7) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 4% simple interest?
(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.
(9) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(10) 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.