Question:
How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?
Correct Answer
$5850
Solution And Explanation
Solution
Given,
Amount (A) = $7020
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
$7020 = P (1 + 4% × 5)
⇒ $7020 = P (1 + 4/100 × 5)
⇒ $7020 = P (1 + 4 × 5/100)
⇒ $7020 = P (1 + 20/100)
⇒ $7020 = P (100 + 20/100)
⇒ $7020 = P × 120/100
⇒ P × 120/100 = $7020
⇒ P = 7020/120/100
⇒ P = 7020 × 100/120
⇒ P = 7020 × 100/120
⇒ P = 702000/120
⇒ P = $5850
Thus, the sum borrowed (P) = $5850 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 7020, then the Principal = 100/120 × 7020
= 100 × 7020/120
= 702000/120
= 5850
Thus, Principal = $5850
Thus, the sum borrowed = $5850 Answer
Similar Questions
(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 7 years.
(2) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(3) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
(4) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.
(5) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(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) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 7% simple interest?
(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 4 years.
(9) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 4% simple interest?
(10) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.