Question:
How much loan did Thomas borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6380 to clear it?
Correct Answer
$5800
Solution And Explanation
Solution
Given,
Amount (A) = $6380
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
$6380 = P (1 + 2% × 5)
⇒ $6380 = P (1 + 2/100 × 5)
⇒ $6380 = P (1 + 2 × 5/100)
⇒ $6380 = P (1 + 10/100)
⇒ $6380 = P (100 + 10/100)
⇒ $6380 = P × 110/100
⇒ P × 110/100 = $6380
⇒ P = 6380/110/100
⇒ P = 6380 × 100/110
⇒ P = 6380 × 100/110
⇒ P = 638000/110
⇒ 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 = 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 6380, then the Principal = 100/110 × 6380
= 100 × 6380/110
= 638000/110
= 5800
Thus, Principal = $5800
Thus, the sum borrowed = $5800 Answer
Similar Questions
(1) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 2% simple interest?
(2) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?
(3) John had to pay $3680 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 7 years.
(5) If Elizabeth paid $4140 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 4 years.
(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 8 years.
(8) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?
(10) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 7 years.