Question:
How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?
Correct Answer
$6500
Solution And Explanation
Solution
Given,
Amount (A) = $7800
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
$7800 = P (1 + 4% × 5)
⇒ $7800 = P (1 + 4/100 × 5)
⇒ $7800 = P (1 + 4 × 5/100)
⇒ $7800 = P (1 + 20/100)
⇒ $7800 = P (100 + 20/100)
⇒ $7800 = P × 120/100
⇒ P × 120/100 = $7800
⇒ P = 7800/120/100
⇒ P = 7800 × 100/120
⇒ P = 7800 × 100/120
⇒ P = 780000/120
⇒ P = $6500
Thus, the sum borrowed (P) = $6500 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 7800, then the Principal = 100/120 × 7800
= 100 × 7800/120
= 780000/120
= 6500
Thus, Principal = $6500
Thus, the sum borrowed = $6500 Answer
Similar Questions
(1) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 2% simple interest?
(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 2% simple interest?
(3) If Steven paid $4968 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.
(5) If David paid $4080 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
(7) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?
(8) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 3 years.
(10) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.