Question:
How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?
Correct Answer
$5050
Solution And Explanation
Solution
Given,
Amount (A) = $5555
Rate of Simple Interest (R) = 2%
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
$5555 = P (1 + 2% × 5)
⇒ $5555 = P (1 + 2/100 × 5)
⇒ $5555 = P (1 + 2 × 5/100)
⇒ $5555 = P (1 + 10/100)
⇒ $5555 = P (100 + 10/100)
⇒ $5555 = P × 110/100
⇒ P × 110/100 = $5555
⇒ P = 5555/110/100
⇒ P = 5555 × 100/110
⇒ P = 5555 × 100/110
⇒ P = 555500/110
⇒ 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 5555, then the Principal = 100/110 × 5555
= 100 × 5555/110
= 555500/110
= 5050
Thus, Principal = $5050
Thus, the sum borrowed = $5050 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.
(2) What amount does John have to pay after 6 years if he takes a loan of $3200 at 4% simple interest?
(3) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.
(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 4 years.
(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.
(7) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
(8) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 7% simple interest?
(9) What amount does John have to pay after 5 years if he takes a loan of $3200 at 8% simple interest?
(10) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?