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) How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?
(2) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 4 years.
(3) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.
(4) If Thomas borrowed $3800 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(5) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 3% simple interest?
(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 4 years.
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 3 years.
(8) Daniel had to pay $4469 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 6% simple interest?
(10) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 7 years.