Question:
How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?
Correct Answer
$7050
Solution And Explanation
Solution
Given,
Amount (A) = $7755
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
$7755 = P (1 + 2% × 5)
⇒ $7755 = P (1 + 2/100 × 5)
⇒ $7755 = P (1 + 2 × 5/100)
⇒ $7755 = P (1 + 10/100)
⇒ $7755 = P (100 + 10/100)
⇒ $7755 = P × 110/100
⇒ P × 110/100 = $7755
⇒ P = 7755/110/100
⇒ P = 7755 × 100/110
⇒ P = 7755 × 100/110
⇒ P = 775500/110
⇒ P = $7050
Thus, the sum borrowed (P) = $7050 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 7755, then the Principal = 100/110 × 7755
= 100 × 7755/110
= 775500/110
= 7050
Thus, Principal = $7050
Thus, the sum borrowed = $7050 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.
(2) How much loan did Mark borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7040 to clear it?
(3) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?
(4) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 4 years.
(5) What amount does William have to pay after 5 years if he takes a loan of $3500 at 10% simple interest?
(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
(7) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 10% simple interest?
(8) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(9) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(10) How much loan did Donna borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8220 to clear it?