Question:
How much loan did Emily borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7762.5 to clear it?
Correct Answer
$6750
Solution And Explanation
Solution
Given,
Amount (A) = $7762.5
Rate of Simple Interest (R) = 3%
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
$7762.5 = P (1 + 3% × 5)
⇒ $7762.5 = P (1 + 3/100 × 5)
⇒ $7762.5 = P (1 + 3 × 5/100)
⇒ $7762.5 = P (1 + 15/100)
⇒ $7762.5 = P (100 + 15/100)
⇒ $7762.5 = P × 115/100
⇒ P × 115/100 = $7762.5
⇒ P = 7762.5/115/100
⇒ P = 7762.5 × 100/115
⇒ P = 7762.5 × 100/115
⇒ P = 776250/115
⇒ 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 7762.5, then the Principal = 100/115 × 7762.5
= 100 × 7762.5/115
= 776250/115
= 6750
Thus, Principal = $6750
Thus, the sum borrowed = $6750 Answer
Similar Questions
(1) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
(2) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(3) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?
(4) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.
(5) How much loan did Charles borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6490 to clear it?
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 7 years.
(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.
(8) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $6936 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 4 years.