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 William have to pay after 6 years if he takes a loan of $3500 at 6% simple interest?
(2) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 8 years.
(3) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.
(4) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.
(5) If Nancy paid $4980 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) How much loan did Timothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8880 to clear it?
(7) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?
(8) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 3 years.
(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 8 years.
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 4 years.