Question:
Mary had to pay $3324.5 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
$3050
Solution And Explanation
Solution
Given,
Amount (A) = $3324.5
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
$3324.5 = P (1 + 3% × 3)
⇒ $3324.5 = P (1 + 3/100 × 3)
⇒ $3324.5 = P (1 + 3 × 3/100)
⇒ $3324.5 = P (1 + 9/100)
⇒ $3324.5 = P (100 + 9/100)
⇒ $3324.5 = P × 109/100
⇒ P × 109/100 = $3324.5
⇒ P = 3324.5/109/100
⇒ P = 3324.5 × 100/109
⇒ P = 3324.5 × 100/109
⇒ P = 332450/109
⇒ P = $3050
Thus, the sum borrowed (P) = $3050 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 3324.5, then the Principal = 100/109 × 3324.5
= 100 × 3324.5/109
= 332450/109
= 3050
Thus, Principal = $3050
Thus, the sum borrowed = $3050 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(3) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.
(4) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
(5) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.
(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 7 years.
(7) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 7% simple interest?
(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 2% simple interest?
(9) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
(10) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.