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 & 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 does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?
(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 7 years.
(3) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.
(4) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 6% simple interest?
(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.
(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 9% simple interest?