Question:
How much loan did Mary borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6060 to clear it?
Correct Answer
$5050
Solution And Explanation
Solution
Given,
Amount (A) = $6060
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
$6060 = P (1 + 4% × 5)
⇒ $6060 = P (1 + 4/100 × 5)
⇒ $6060 = P (1 + 4 × 5/100)
⇒ $6060 = P (1 + 20/100)
⇒ $6060 = P (100 + 20/100)
⇒ $6060 = P × 120/100
⇒ P × 120/100 = $6060
⇒ P = 6060/120/100
⇒ P = 6060 × 100/120
⇒ P = 6060 × 100/120
⇒ P = 606000/120
⇒ P = $5050
Thus, the sum borrowed (P) = $5050 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 6060, then the Principal = 100/120 × 6060
= 100 × 6060/120
= 606000/120
= 5050
Thus, Principal = $5050
Thus, the sum borrowed = $5050 Answer
Similar Questions
(1) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 3 years.
(2) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.
(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 7 years.
(4) 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?
(5) How much loan did Linda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6152.5 to clear it?
(6) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 4 years.
(7) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.
(8) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
(9) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 2% simple interest?
(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 8 years.