Question:
Sarah had to pay $4081 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
$3850
Solution And Explanation
Solution
Given,
Amount (A) = $4081
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
$4081 = P (1 + 2% × 3)
⇒ $4081 = P (1 + 2/100 × 3)
⇒ $4081 = P (1 + 2 × 3/100)
⇒ $4081 = P (1 + 6/100)
⇒ $4081 = P (100 + 6/100)
⇒ $4081 = P × 106/100
⇒ P × 106/100 = $4081
⇒ P = 4081/106/100
⇒ P = 4081 × 100/106
⇒ P = 4081 × 100/106
⇒ P = 408100/106
⇒ P = $3850
Thus, the sum borrowed (P) = $3850 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 4081, then the Principal = 100/106 × 4081
= 100 × 4081/106
= 408100/106
= 3850
Thus, Principal = $3850
Thus, the sum borrowed = $3850 Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.
(2) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 2% simple interest?
(3) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.
(4) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.
(5) 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.
(6) How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?
(7) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.
(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.
(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 7 years.
(10) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?