Question:
How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?
Correct Answer
$5400
Solution And Explanation
Solution
Given,
Amount (A) = $6210
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
$6210 = P (1 + 3% × 5)
⇒ $6210 = P (1 + 3/100 × 5)
⇒ $6210 = P (1 + 3 × 5/100)
⇒ $6210 = P (1 + 15/100)
⇒ $6210 = P (100 + 15/100)
⇒ $6210 = P × 115/100
⇒ P × 115/100 = $6210
⇒ P = 6210/115/100
⇒ P = 6210 × 100/115
⇒ P = 6210 × 100/115
⇒ P = 621000/115
⇒ P = $5400
Thus, the sum borrowed (P) = $5400 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 6210, then the Principal = 100/115 × 6210
= 100 × 6210/115
= 621000/115
= 5400
Thus, Principal = $5400
Thus, the sum borrowed = $5400 Answer
Similar Questions
(1) Michael had to pay $3696 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(3) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 7 years.
(5) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7980 to clear it?
(7) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 8 years.
(9) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?
(10) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.