Question:
How much loan did Anthony borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7245 to clear it?
Correct Answer
$6300
Solution And Explanation
Solution
Given,
Amount (A) = $7245
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
$7245 = P (1 + 3% × 5)
⇒ $7245 = P (1 + 3/100 × 5)
⇒ $7245 = P (1 + 3 × 5/100)
⇒ $7245 = P (1 + 15/100)
⇒ $7245 = P (100 + 15/100)
⇒ $7245 = P × 115/100
⇒ P × 115/100 = $7245
⇒ P = 7245/115/100
⇒ P = 7245 × 100/115
⇒ P = 7245 × 100/115
⇒ P = 724500/115
⇒ P = $6300
Thus, the sum borrowed (P) = $6300 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 7245, then the Principal = 100/115 × 7245
= 100 × 7245/115
= 724500/115
= 6300
Thus, Principal = $6300
Thus, the sum borrowed = $6300 Answer
Similar Questions
(1) Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.
(3) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.
(5) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 5% simple interest?
(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 8% simple interest.
(7) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 10% simple interest?
(8) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
(9) Sandra had to pay $4850.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) Sandra had to pay $5117.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.