Question:
How much loan did Ashley borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7860 to clear it?
Correct Answer
$6550
Solution And Explanation
Solution
Given,
Amount (A) = $7860
Rate of Simple Interest (R) = 4%
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
$7860 = P (1 + 4% × 5)
⇒ $7860 = P (1 + 4/100 × 5)
⇒ $7860 = P (1 + 4 × 5/100)
⇒ $7860 = P (1 + 20/100)
⇒ $7860 = P (100 + 20/100)
⇒ $7860 = P × 120/100
⇒ P × 120/100 = $7860
⇒ P = 7860/120/100
⇒ P = 7860 × 100/120
⇒ P = 7860 × 100/120
⇒ P = 786000/120
⇒ P = $6550
Thus, the sum borrowed (P) = $6550 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 7860, then the Principal = 100/120 × 7860
= 100 × 7860/120
= 786000/120
= 6550
Thus, Principal = $6550
Thus, the sum borrowed = $6550 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 8 years.
(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 7 years.
(4) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 2% simple interest.
(5) In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?
(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 7 years.
(7) How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?
(8) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?
(9) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.
(10) What amount will be due after 2 years if David borrowed a sum of $3200 at a 6% simple interest?