Question:
How much loan did Thomas borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6670 to clear it?
Correct Answer
$5800
Solution And Explanation
Solution
Given,
Amount (A) = $6670
Rate of Simple Interest (R) = 3%
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
$6670 = P (1 + 3% × 5)
⇒ $6670 = P (1 + 3/100 × 5)
⇒ $6670 = P (1 + 3 × 5/100)
⇒ $6670 = P (1 + 15/100)
⇒ $6670 = P (100 + 15/100)
⇒ $6670 = P × 115/100
⇒ P × 115/100 = $6670
⇒ P = 6670/115/100
⇒ P = 6670 × 100/115
⇒ P = 6670 × 100/115
⇒ P = 667000/115
⇒ P = $5800
Thus, the sum borrowed (P) = $5800 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 6670, then the Principal = 100/115 × 6670
= 100 × 6670/115
= 667000/115
= 5800
Thus, Principal = $5800
Thus, the sum borrowed = $5800 Answer
Similar Questions
(1) What amount will be due after 2 years if James borrowed a sum of $3000 at a 4% simple interest?
(2) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 7% simple interest.
(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 8 years.
(4) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 3 years.
(5) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?
(6) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 4% simple interest?
(7) Betty had to pay $4887.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Sarah had to pay $4427.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 9% simple interest?
(10) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 8% simple interest.