Question:
How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?
Correct Answer
$6450
Solution And Explanation
Solution
Given,
Amount (A) = $7417.5
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
$7417.5 = P (1 + 3% × 5)
⇒ $7417.5 = P (1 + 3/100 × 5)
⇒ $7417.5 = P (1 + 3 × 5/100)
⇒ $7417.5 = P (1 + 15/100)
⇒ $7417.5 = P (100 + 15/100)
⇒ $7417.5 = P × 115/100
⇒ P × 115/100 = $7417.5
⇒ P = 7417.5/115/100
⇒ P = 7417.5 × 100/115
⇒ P = 7417.5 × 100/115
⇒ P = 741750/115
⇒ P = $6450
Thus, the sum borrowed (P) = $6450 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 7417.5, then the Principal = 100/115 × 7417.5
= 100 × 7417.5/115
= 741750/115
= 6450
Thus, Principal = $6450
Thus, the sum borrowed = $6450 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.
(3) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 9% simple interest?
(4) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
(5) How much loan did Margaret borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6985 to clear it?
(6) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 4 years.
(7) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?
(8) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 3 years.
(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
(10) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 3 years.