Question:
How much loan did Amanda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7865 to clear it?
Correct Answer
$7150
Solution And Explanation
Solution
Given,
Amount (A) = $7865
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
$7865 = P (1 + 2% × 5)
⇒ $7865 = P (1 + 2/100 × 5)
⇒ $7865 = P (1 + 2 × 5/100)
⇒ $7865 = P (1 + 10/100)
⇒ $7865 = P (100 + 10/100)
⇒ $7865 = P × 110/100
⇒ P × 110/100 = $7865
⇒ P = 7865/110/100
⇒ P = 7865 × 100/110
⇒ P = 7865 × 100/110
⇒ P = 786500/110
⇒ P = $7150
Thus, the sum borrowed (P) = $7150 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 7865, then the Principal = 100/110 × 7865
= 100 × 7865/110
= 786500/110
= 7150
Thus, Principal = $7150
Thus, the sum borrowed = $7150 Answer
Similar Questions
(1) What amount does David have to pay after 6 years if he takes a loan of $3400 at 3% simple interest?
(2) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 3 years.
(3) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.
(4) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 7% simple interest?
(5) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?
(6) If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.
(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 8 years.
(9) How much loan did Mary borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5807.5 to clear it?
(10) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?