Question:
How much loan did Edward borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8740 to clear it?
Correct Answer
$7600
Solution And Explanation
Solution
Given,
Amount (A) = $8740
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
$8740 = P (1 + 3% × 5)
⇒ $8740 = P (1 + 3/100 × 5)
⇒ $8740 = P (1 + 3 × 5/100)
⇒ $8740 = P (1 + 15/100)
⇒ $8740 = P (100 + 15/100)
⇒ $8740 = P × 115/100
⇒ P × 115/100 = $8740
⇒ P = 8740/115/100
⇒ P = 8740 × 100/115
⇒ P = 8740 × 100/115
⇒ P = 874000/115
⇒ P = $7600
Thus, the sum borrowed (P) = $7600 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 8740, then the Principal = 100/115 × 8740
= 100 × 8740/115
= 874000/115
= 7600
Thus, Principal = $7600
Thus, the sum borrowed = $7600 Answer
Similar Questions
(1) In how much time a principal of $3000 will amount to $3270 at a simple interest of 3% per annum?
(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 8 years.
(3) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 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 $8296 to clear the loan, then find the time period of the loan.
(5) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.
(6) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.
(7) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.
(8) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.
(10) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 9% simple interest?