Question:
How much loan did Ronald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8250 to clear it?
Correct Answer
$7500
Solution And Explanation
Solution
Given,
Amount (A) = $8250
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
$8250 = P (1 + 2% × 5)
⇒ $8250 = P (1 + 2/100 × 5)
⇒ $8250 = P (1 + 2 × 5/100)
⇒ $8250 = P (1 + 10/100)
⇒ $8250 = P (100 + 10/100)
⇒ $8250 = P × 110/100
⇒ P × 110/100 = $8250
⇒ P = 8250/110/100
⇒ P = 8250 × 100/110
⇒ P = 8250 × 100/110
⇒ P = 825000/110
⇒ P = $7500
Thus, the sum borrowed (P) = $7500 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 8250, then the Principal = 100/110 × 8250
= 100 × 8250/110
= 825000/110
= 7500
Thus, Principal = $7500
Thus, the sum borrowed = $7500 Answer
Similar Questions
(1) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 6% simple interest?
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 8 years.
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 8 years.
(4) How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?
(5) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 6% simple interest?
(6) How much loan did James borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6000 to clear it?
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.
(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 3 years.
(9) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) What amount does John have to pay after 5 years if he takes a loan of $3200 at 7% simple interest?