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) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.
(2) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 8% simple interest.
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 8 years.
(4) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.
(5) Christopher had to pay $4240 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?
(7) How much loan did David borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5940 to clear it?
(8) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.
(9) In how much time a principal of $3000 will amount to $3270 at a simple interest of 3% per annum?
(10) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 7% simple interest?