Question:
Michelle had to pay $5395.5 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
$4950
Solution And Explanation
Solution
Given,
Amount (A) = $5395.5
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
$5395.5 = P (1 + 3% × 3)
⇒ $5395.5 = P (1 + 3/100 × 3)
⇒ $5395.5 = P (1 + 3 × 3/100)
⇒ $5395.5 = P (1 + 9/100)
⇒ $5395.5 = P (100 + 9/100)
⇒ $5395.5 = P × 109/100
⇒ P × 109/100 = $5395.5
⇒ P = 5395.5/109/100
⇒ P = 5395.5 × 100/109
⇒ P = 5395.5 × 100/109
⇒ P = 539550/109
⇒ P = $4950
Thus, the sum borrowed (P) = $4950 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 5395.5, then the Principal = 100/109 × 5395.5
= 100 × 5395.5/109
= 539550/109
= 4950
Thus, Principal = $4950
Thus, the sum borrowed = $4950 Answer
Similar Questions
(1) If Linda borrowed $3350 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.
(3) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.
(4) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 5% simple interest.
(6) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.
(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 3 years.
(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.
(10) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.