Question:
Ashley had to pay $4959.5 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
$4550
Solution And Explanation
Solution
Given,
Amount (A) = $4959.5
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
$4959.5 = P (1 + 3% × 3)
⇒ $4959.5 = P (1 + 3/100 × 3)
⇒ $4959.5 = P (1 + 3 × 3/100)
⇒ $4959.5 = P (1 + 9/100)
⇒ $4959.5 = P (100 + 9/100)
⇒ $4959.5 = P × 109/100
⇒ P × 109/100 = $4959.5
⇒ P = 4959.5/109/100
⇒ P = 4959.5 × 100/109
⇒ P = 4959.5 × 100/109
⇒ P = 495950/109
⇒ P = $4550
Thus, the sum borrowed (P) = $4550 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 4959.5, then the Principal = 100/109 × 4959.5
= 100 × 4959.5/109
= 495950/109
= 4550
Thus, Principal = $4550
Thus, the sum borrowed = $4550 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.
(2) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
(3) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
(4) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 3 years.
(5) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 3 years.
(9) Emily had to pay $5320 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 4 years.