Question:
How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?
Correct Answer
$5550
Solution And Explanation
Solution
Given,
Amount (A) = $6105
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
$6105 = P (1 + 2% × 5)
⇒ $6105 = P (1 + 2/100 × 5)
⇒ $6105 = P (1 + 2 × 5/100)
⇒ $6105 = P (1 + 10/100)
⇒ $6105 = P (100 + 10/100)
⇒ $6105 = P × 110/100
⇒ P × 110/100 = $6105
⇒ P = 6105/110/100
⇒ P = 6105 × 100/110
⇒ P = 6105 × 100/110
⇒ P = 610500/110
⇒ P = $5550
Thus, the sum borrowed (P) = $5550 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 6105, then the Principal = 100/110 × 6105
= 100 × 6105/110
= 610500/110
= 5550
Thus, Principal = $5550
Thus, the sum borrowed = $5550 Answer
Similar Questions
(1) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?
(2) Richard had to pay $4140 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 7 years.
(4) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(5) If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 8 years.
(7) In how much time a principal of $3000 will amount to $3450 at a simple interest of 3% per annum?
(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 4 years.
(9) If Joshua paid $5684 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.