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) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 4 years.
(2) How much loan did Karen borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6545 to clear it?
(3) What amount does John have to pay after 5 years if he takes a loan of $3200 at 9% simple interest?
(4) How much loan did Amanda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8222.5 to clear it?
(5) What amount does David have to pay after 6 years if he takes a loan of $3400 at 7% simple interest?
(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 8 years.
(7) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 7 years.
(9) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
(10) In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?