Question:
Jessica had to pay $3975 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
$3750
Solution And Explanation
Solution
Given,
Amount (A) = $3975
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
$3975 = P (1 + 2% × 3)
⇒ $3975 = P (1 + 2/100 × 3)
⇒ $3975 = P (1 + 2 × 3/100)
⇒ $3975 = P (1 + 6/100)
⇒ $3975 = P (100 + 6/100)
⇒ $3975 = P × 106/100
⇒ P × 106/100 = $3975
⇒ P = 3975/106/100
⇒ P = 3975 × 100/106
⇒ P = 3975 × 100/106
⇒ P = 397500/106
⇒ P = $3750
Thus, the sum borrowed (P) = $3750 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 3975, then the Principal = 100/106 × 3975
= 100 × 3975/106
= 397500/106
= 3750
Thus, Principal = $3750
Thus, the sum borrowed = $3750 Answer
Similar Questions
(1) What amount does David have to pay after 5 years if he takes a loan of $3400 at 2% simple interest?
(2) If Robert borrowed $3100 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(3) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 4 years.
(5) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 4 years.
(6) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 3 years.
(7) What amount does John have to pay after 5 years if he takes a loan of $3200 at 10% simple interest?
(8) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?
(9) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $8976 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?