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 after 10 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.
(2) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.
(3) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?
(4) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 4 years.
(6) Susan had to pay $3869 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?
(8) What amount will be due after 2 years if John borrowed a sum of $3100 at a 8% simple interest?
(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 6% simple interest?
(10) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.