Question:
Mark had to pay $4664 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
Correct Answer
$4400
Solution And Explanation
Solution
Given,
Amount (A) = $4664
Rate of Simple Interest (R) = 2%
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
$4664 = P (1 + 2% × 3)
⇒ $4664 = P (1 + 2/100 × 3)
⇒ $4664 = P (1 + 2 × 3/100)
⇒ $4664 = P (1 + 6/100)
⇒ $4664 = P (100 + 6/100)
⇒ $4664 = P × 106/100
⇒ P × 106/100 = $4664
⇒ P = 4664/106/100
⇒ P = 4664 × 100/106
⇒ P = 4664 × 100/106
⇒ P = 466400/106
⇒ 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 6
Thus, simple interest for 3 years = 6
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 6 = 106
Calculation of the Principal
Now,
∵ If the Amount is 106, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/106
∴ If the Amount is 4664, then the Principal = 100/106 × 4664
= 100 × 4664/106
= 466400/106
= 4400
Thus, Principal = $4400
Thus, the sum borrowed = $4400 Answer
Similar Questions
(1) 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.
(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 7 years.
(3) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 6% simple interest?
(4) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 3 years.
(6) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(7) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?
(8) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 3 years.
(9) How much loan did Christopher borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6900 to clear it?
(10) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.