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) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.
(2) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.
(4) If Linda borrowed $3350 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.
(6) If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Sandra had to pay $4850.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 6% simple interest?
(9) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 4% simple interest?
(10) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.