Question:
How much loan did Ryan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8690 to clear it?
Correct Answer
$7900
Solution And Explanation
Solution
Given,
Amount (A) = $8690
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
$8690 = P (1 + 2% × 5)
⇒ $8690 = P (1 + 2/100 × 5)
⇒ $8690 = P (1 + 2 × 5/100)
⇒ $8690 = P (1 + 10/100)
⇒ $8690 = P (100 + 10/100)
⇒ $8690 = P × 110/100
⇒ P × 110/100 = $8690
⇒ P = 8690/110/100
⇒ P = 8690 × 100/110
⇒ P = 8690 × 100/110
⇒ P = 869000/110
⇒ P = $7900
Thus, the sum borrowed (P) = $7900 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 8690, then the Principal = 100/110 × 8690
= 100 × 8690/110
= 869000/110
= 7900
Thus, Principal = $7900
Thus, the sum borrowed = $7900 Answer
Similar Questions
(1) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.
(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 7 years.
(3) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.
(5) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.
(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 4 years.
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 8 years.
(8) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(9) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 3% simple interest?
(10) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?