Question:
How much loan did Jason borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9240 to clear it?
Correct Answer
$7700
Solution And Explanation
Solution
Given,
Amount (A) = $9240
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
$9240 = P (1 + 4% × 5)
⇒ $9240 = P (1 + 4/100 × 5)
⇒ $9240 = P (1 + 4 × 5/100)
⇒ $9240 = P (1 + 20/100)
⇒ $9240 = P (100 + 20/100)
⇒ $9240 = P × 120/100
⇒ P × 120/100 = $9240
⇒ P = 9240/120/100
⇒ P = 9240 × 100/120
⇒ P = 9240 × 100/120
⇒ P = 924000/120
⇒ P = $7700
Thus, the sum borrowed (P) = $7700 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 9240, then the Principal = 100/120 × 9240
= 100 × 9240/120
= 924000/120
= 7700
Thus, Principal = $7700
Thus, the sum borrowed = $7700 Answer
Similar Questions
(1) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 8% simple interest?
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 8 years.
(3) How much loan did Donald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8125 to clear it?
(4) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.
(6) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 7 years.
(8) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 6% simple interest?
(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 7 years.
(10) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6812.5 to clear it?