Question:
How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?
Correct Answer
$5850
Solution And Explanation
Solution
Given,
Amount (A) = $6727.5
Rate of Simple Interest (R) = 3%
Time (T) = 5 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
$6727.5 = P (1 + 3% × 5)
⇒ $6727.5 = P (1 + 3/100 × 5)
⇒ $6727.5 = P (1 + 3 × 5/100)
⇒ $6727.5 = P (1 + 15/100)
⇒ $6727.5 = P (100 + 15/100)
⇒ $6727.5 = P × 115/100
⇒ P × 115/100 = $6727.5
⇒ P = 6727.5/115/100
⇒ P = 6727.5 × 100/115
⇒ P = 6727.5 × 100/115
⇒ P = 672750/115
⇒ P = $5850
Thus, the sum borrowed (P) = $5850 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 = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 3 = 15
Thus, simple interest for 5 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 6727.5, then the Principal = 100/115 × 6727.5
= 100 × 6727.5/115
= 672750/115
= 5850
Thus, Principal = $5850
Thus, the sum borrowed = $5850 Answer
Similar Questions
(1) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.
(3) In how much time a principal of $3100 will amount to $3472 at a simple interest of 4% per annum?
(4) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 3% simple interest?
(5) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?
(6) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 6% simple interest?
(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 7 years.
(8) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?
(9) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.
(10) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.