Question:
Margaret had to pay $5002.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
Correct Answer
$4350
Solution And Explanation
Solution
Given,
Amount (A) = $5002.5
Rate of Simple Interest (R) = 5%
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
$5002.5 = P (1 + 5% × 3)
⇒ $5002.5 = P (1 + 5/100 × 3)
⇒ $5002.5 = P (1 + 5 × 3/100)
⇒ $5002.5 = P (1 + 15/100)
⇒ $5002.5 = P (100 + 15/100)
⇒ $5002.5 = P × 115/100
⇒ P × 115/100 = $5002.5
⇒ P = 5002.5/115/100
⇒ P = 5002.5 × 100/115
⇒ P = 5002.5 × 100/115
⇒ P = 500250/115
⇒ P = $4350
Thus, the sum borrowed (P) = $4350 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 15
Thus, simple interest for 3 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 5002.5, then the Principal = 100/115 × 5002.5
= 100 × 5002.5/115
= 500250/115
= 4350
Thus, Principal = $4350
Thus, the sum borrowed = $4350 Answer
Similar Questions
(1) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 6% simple interest?
(2) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $10000 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.
(4) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 3 years.
(5) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 4 years.
(6) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 3 years.
(7) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 8 years.
(9) What amount will be due after 2 years if David borrowed a sum of $3200 at a 9% simple interest?
(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 7 years.