Question:
How much loan did Emily borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8100 to clear it?
Correct Answer
$6750
Solution And Explanation
Solution
Given,
Amount (A) = $8100
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
$8100 = P (1 + 4% × 5)
⇒ $8100 = P (1 + 4/100 × 5)
⇒ $8100 = P (1 + 4 × 5/100)
⇒ $8100 = P (1 + 20/100)
⇒ $8100 = P (100 + 20/100)
⇒ $8100 = P × 120/100
⇒ P × 120/100 = $8100
⇒ P = 8100/120/100
⇒ P = 8100 × 100/120
⇒ P = 8100 × 100/120
⇒ P = 810000/120
⇒ 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 = 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 8100, then the Principal = 100/120 × 8100
= 100 × 8100/120
= 810000/120
= 6750
Thus, Principal = $6750
Thus, the sum borrowed = $6750 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.
(2) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 3 years.
(3) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 4 years.
(4) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.
(5) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.
(6) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.
(7) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 7% simple interest?
(8) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(9) Margaret had to pay $4872 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 8 years.