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) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?
(2) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 4% simple interest?
(3) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.
(5) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 10% simple interest?
(6) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3100 will amount to $3720 at a simple interest of 5% per annum?
(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 8 years.
(9) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 8 years.
(10) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?