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 Michael borrowed a sum of $5300 at 8% simple interest for 8 years.
(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 3 years.
(3) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?
(4) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.
(5) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 7 years.
(7) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 3 years.
(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 7 years.
(9) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
(10) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 8% simple interest?