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) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 8 years.
(3) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 7% simple interest?
(4) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
(5) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 3% simple interest?
(6) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 9% simple interest?
(7) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.
(8) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 3 years.
(9) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 10% simple interest?
(10) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?