Question:
Donald had to pay $4770 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
$4500
Solution And Explanation
Solution
Given,
Amount (A) = $4770
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
$4770 = P (1 + 2% × 3)
⇒ $4770 = P (1 + 2/100 × 3)
⇒ $4770 = P (1 + 2 × 3/100)
⇒ $4770 = P (1 + 6/100)
⇒ $4770 = P (100 + 6/100)
⇒ $4770 = P × 106/100
⇒ P × 106/100 = $4770
⇒ P = 4770/106/100
⇒ P = 4770 × 100/106
⇒ P = 4770 × 100/106
⇒ P = 477000/106
⇒ P = $4500
Thus, the sum borrowed (P) = $4500 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 4770, then the Principal = 100/106 × 4770
= 100 × 4770/106
= 477000/106
= 4500
Thus, Principal = $4500
Thus, the sum borrowed = $4500 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.
(2) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?
(3) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?
(4) Linda had to pay $3651.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 7 years.
(7) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 8 years.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 7 years.
(9) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.
(10) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.