Question:
How much loan did Kenneth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7700 to clear it?
Correct Answer
$7000
Solution And Explanation
Solution
Given,
Amount (A) = $7700
Rate of Simple Interest (R) = 2%
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
$7700 = P (1 + 2% × 5)
⇒ $7700 = P (1 + 2/100 × 5)
⇒ $7700 = P (1 + 2 × 5/100)
⇒ $7700 = P (1 + 10/100)
⇒ $7700 = P (100 + 10/100)
⇒ $7700 = P × 110/100
⇒ P × 110/100 = $7700
⇒ P = 7700/110/100
⇒ P = 7700 × 100/110
⇒ P = 7700 × 100/110
⇒ P = 770000/110
⇒ P = $7000
Thus, the sum borrowed (P) = $7000 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 7700, then the Principal = 100/110 × 7700
= 100 × 7700/110
= 770000/110
= 7000
Thus, Principal = $7000
Thus, the sum borrowed = $7000 Answer
Similar Questions
(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 7 years.
(2) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 8% simple interest?
(4) In how much time a principal of $3000 will amount to $3240 at a simple interest of 4% per annum?
(5) How much loan did Christopher borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6900 to clear it?
(6) How much loan did Melissa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8452.5 to clear it?
(7) If Joseph borrowed $3700 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(8) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 8% simple interest?
(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
(10) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 2% simple interest?