Question:
How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?
Correct Answer
$7300
Solution And Explanation
Solution
Given,
Amount (A) = $8395
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
$8395 = P (1 + 3% × 5)
⇒ $8395 = P (1 + 3/100 × 5)
⇒ $8395 = P (1 + 3 × 5/100)
⇒ $8395 = P (1 + 15/100)
⇒ $8395 = P (100 + 15/100)
⇒ $8395 = P × 115/100
⇒ P × 115/100 = $8395
⇒ P = 8395/115/100
⇒ P = 8395 × 100/115
⇒ P = 8395 × 100/115
⇒ P = 839500/115
⇒ P = $7300
Thus, the sum borrowed (P) = $7300 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 8395, then the Principal = 100/115 × 8395
= 100 × 8395/115
= 839500/115
= 7300
Thus, Principal = $7300
Thus, the sum borrowed = $7300 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 8 years.
(3) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?
(4) What amount does William have to pay after 6 years if he takes a loan of $3500 at 9% simple interest?
(5) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?
(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 8 years.
(7) Robert had to pay $3286 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 4 years.
(9) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.
(10) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.