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) How much loan did Thomas borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6960 to clear it?
(2) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.
(3) Ashley had to pay $5096 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
(5) How much loan did Jessica borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6900 to clear it?
(6) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?
(7) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.
(9) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 7 years.
(10) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 2% simple interest.