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) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 8% simple interest?
(2) How much loan did Christopher borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7500 to clear it?
(3) Linda had to pay $3651.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Calculate the amount due if Susan borrowed a sum of $3650 at 8% simple interest for 3 years.
(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 3 years.
(6) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 4% simple interest?
(7) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8797.5 to clear it?
(8) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 10% simple interest?
(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 3 years.
(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 8 years.