Question:
How much loan did Rebecca borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9180 to clear it?
Correct Answer
$7650
Solution And Explanation
Solution
Given,
Amount (A) = $9180
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
$9180 = P (1 + 4% × 5)
⇒ $9180 = P (1 + 4/100 × 5)
⇒ $9180 = P (1 + 4 × 5/100)
⇒ $9180 = P (1 + 20/100)
⇒ $9180 = P (100 + 20/100)
⇒ $9180 = P × 120/100
⇒ P × 120/100 = $9180
⇒ P = 9180/120/100
⇒ P = 9180 × 100/120
⇒ P = 9180 × 100/120
⇒ P = 918000/120
⇒ P = $7650
Thus, the sum borrowed (P) = $7650 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 9180, then the Principal = 100/120 × 9180
= 100 × 9180/120
= 918000/120
= 7650
Thus, Principal = $7650
Thus, the sum borrowed = $7650 Answer
Similar Questions
(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 7 years.
(2) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(3) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?
(4) If Elizabeth borrowed $3450 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(5) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 7 years.
(7) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 9% simple interest?
(8) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.
(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.