Question:
How much loan did Ronald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9000 to clear it?
Correct Answer
$7500
Solution And Explanation
Solution
Given,
Amount (A) = $9000
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
$9000 = P (1 + 4% × 5)
⇒ $9000 = P (1 + 4/100 × 5)
⇒ $9000 = P (1 + 4 × 5/100)
⇒ $9000 = P (1 + 20/100)
⇒ $9000 = P (100 + 20/100)
⇒ $9000 = P × 120/100
⇒ P × 120/100 = $9000
⇒ P = 9000/120/100
⇒ P = 9000 × 100/120
⇒ P = 9000 × 100/120
⇒ P = 900000/120
⇒ P = $7500
Thus, the sum borrowed (P) = $7500 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 9000, then the Principal = 100/120 × 9000
= 100 × 9000/120
= 900000/120
= 7500
Thus, Principal = $7500
Thus, the sum borrowed = $7500 Answer
Similar Questions
(1) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 3 years.
(2) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 10% simple interest?
(3) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?
(4) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(5) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 5% simple interest?
(6) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?
(7) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 6% simple interest?
(8) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.
(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.