Question:
Sarah had to pay $4196.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
Correct Answer
$3850
Solution And Explanation
Solution
Given,
Amount (A) = $4196.5
Rate of Simple Interest (R) = 3%
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
$4196.5 = P (1 + 3% × 3)
⇒ $4196.5 = P (1 + 3/100 × 3)
⇒ $4196.5 = P (1 + 3 × 3/100)
⇒ $4196.5 = P (1 + 9/100)
⇒ $4196.5 = P (100 + 9/100)
⇒ $4196.5 = P × 109/100
⇒ P × 109/100 = $4196.5
⇒ P = 4196.5/109/100
⇒ P = 4196.5 × 100/109
⇒ P = 4196.5 × 100/109
⇒ P = 419650/109
⇒ 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 9
Thus, simple interest for 3 years = 9
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 9 = 109
Calculation of the Principal
Now,
∵ If the Amount is 109, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/109
∴ If the Amount is 4196.5, then the Principal = 100/109 × 4196.5
= 100 × 4196.5/109
= 419650/109
= 3850
Thus, Principal = $3850
Thus, the sum borrowed = $3850 Answer
Similar Questions
(1) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 4 years.
(2) How much loan did Charles borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7080 to clear it?
(3) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if David borrowed a sum of $3200 at a 8% simple interest?
(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 7 years.
(6) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 4 years.
(7) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 10% simple interest?
(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 7 years.
(9) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 4% simple interest?