Question:
How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?
Correct Answer
$7400
Solution And Explanation
Solution
Given,
Amount (A) = $8140
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
$8140 = P (1 + 2% × 5)
⇒ $8140 = P (1 + 2/100 × 5)
⇒ $8140 = P (1 + 2 × 5/100)
⇒ $8140 = P (1 + 10/100)
⇒ $8140 = P (100 + 10/100)
⇒ $8140 = P × 110/100
⇒ P × 110/100 = $8140
⇒ P = 8140/110/100
⇒ P = 8140 × 100/110
⇒ P = 8140 × 100/110
⇒ P = 814000/110
⇒ P = $7400
Thus, the sum borrowed (P) = $7400 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 8140, then the Principal = 100/110 × 8140
= 100 × 8140/110
= 814000/110
= 7400
Thus, Principal = $7400
Thus, the sum borrowed = $7400 Answer
Similar Questions
(1) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 4 years.
(2) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 3 years.
(3) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
(4) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.
(6) How much loan did Barbara borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6382.5 to clear it?
(7) How much loan did Jason borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9240 to clear it?
(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 3 years.
(9) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.
(10) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.