Question:
How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?
Correct Answer
$6750
Solution And Explanation
Solution
Given,
Amount (A) = $7425
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
$7425 = P (1 + 2% × 5)
⇒ $7425 = P (1 + 2/100 × 5)
⇒ $7425 = P (1 + 2 × 5/100)
⇒ $7425 = P (1 + 10/100)
⇒ $7425 = P (100 + 10/100)
⇒ $7425 = P × 110/100
⇒ P × 110/100 = $7425
⇒ P = 7425/110/100
⇒ P = 7425 × 100/110
⇒ P = 7425 × 100/110
⇒ P = 742500/110
⇒ P = $6750
Thus, the sum borrowed (P) = $6750 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 7425, then the Principal = 100/110 × 7425
= 100 × 7425/110
= 742500/110
= 6750
Thus, Principal = $6750
Thus, the sum borrowed = $6750 Answer
Similar Questions
(1) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?
(3) Sarah had to pay $4427.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.
(5) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 4 years.
(6) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 6% simple interest?
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 4 years.
(8) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.
(10) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.