Question:
Margaret had to pay $4611 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
$4350
Solution And Explanation
Solution
Given,
Amount (A) = $4611
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
$4611 = P (1 + 2% × 3)
⇒ $4611 = P (1 + 2/100 × 3)
⇒ $4611 = P (1 + 2 × 3/100)
⇒ $4611 = P (1 + 6/100)
⇒ $4611 = P (100 + 6/100)
⇒ $4611 = P × 106/100
⇒ P × 106/100 = $4611
⇒ P = 4611/106/100
⇒ P = 4611 × 100/106
⇒ P = 4611 × 100/106
⇒ P = 461100/106
⇒ P = $4350
Thus, the sum borrowed (P) = $4350 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 4611, then the Principal = 100/106 × 4611
= 100 × 4611/106
= 461100/106
= 4350
Thus, Principal = $4350
Thus, the sum borrowed = $4350 Answer
Similar Questions
(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 4 years.
(2) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 3 years.
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.
(4) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.
(5) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 9% simple interest?
(6) If Patricia paid $3654 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 6% simple interest?
(8) In how much time a principal of $3000 will amount to $3300 at a simple interest of 5% per annum?
(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 3 years.
(10) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.