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) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.
(2) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(3) How much loan did Steven borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7590 to clear it?
(4) In how much time a principal of $3000 will amount to $3270 at a simple interest of 3% per annum?
(5) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 10% simple interest?
(6) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.
(7) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.
(8) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 3% simple interest?
(9) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 9% simple interest?
(10) How much loan did Jason borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9240 to clear it?