Question:
How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?
Correct Answer
$6700
Solution And Explanation
Solution
Given,
Amount (A) = $7705
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
$7705 = P (1 + 3% × 5)
⇒ $7705 = P (1 + 3/100 × 5)
⇒ $7705 = P (1 + 3 × 5/100)
⇒ $7705 = P (1 + 15/100)
⇒ $7705 = P (100 + 15/100)
⇒ $7705 = P × 115/100
⇒ P × 115/100 = $7705
⇒ P = 7705/115/100
⇒ P = 7705 × 100/115
⇒ P = 7705 × 100/115
⇒ P = 770500/115
⇒ P = $6700
Thus, the sum borrowed (P) = $6700 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 7705, then the Principal = 100/115 × 7705
= 100 × 7705/115
= 770500/115
= 6700
Thus, Principal = $6700
Thus, the sum borrowed = $6700 Answer
Similar Questions
(1) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.
(3) How much loan did Melissa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8820 to clear it?
(4) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 4 years.
(6) How much loan did Charles borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7375 to clear it?
(7) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 8 years.
(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 3 years.
(10) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.