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) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 7 years.
(2) How much loan did Edward borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8740 to clear it?
(3) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(5) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 4 years.
(7) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?
(8) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 3 years.
(10) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.