Question:
How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?
Correct Answer
$7200
Solution And Explanation
Solution
Given,
Amount (A) = $8280
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
$8280 = P (1 + 3% × 5)
⇒ $8280 = P (1 + 3/100 × 5)
⇒ $8280 = P (1 + 3 × 5/100)
⇒ $8280 = P (1 + 15/100)
⇒ $8280 = P (100 + 15/100)
⇒ $8280 = P × 115/100
⇒ P × 115/100 = $8280
⇒ P = 8280/115/100
⇒ P = 8280 × 100/115
⇒ P = 8280 × 100/115
⇒ P = 828000/115
⇒ P = $7200
Thus, the sum borrowed (P) = $7200 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 8280, then the Principal = 100/115 × 8280
= 100 × 8280/115
= 828000/115
= 7200
Thus, Principal = $7200
Thus, the sum borrowed = $7200 Answer
Similar Questions
(1) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.
(2) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(3) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?
(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 3 years.
(5) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 3 years.
(6) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
(7) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.
(8) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(9) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 2% simple interest?
(10) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.