Question:
How much loan did Andrew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7820 to clear it?
Correct Answer
$6800
Solution And Explanation
Solution
Given,
Amount (A) = $7820
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
$7820 = P (1 + 3% × 5)
⇒ $7820 = P (1 + 3/100 × 5)
⇒ $7820 = P (1 + 3 × 5/100)
⇒ $7820 = P (1 + 15/100)
⇒ $7820 = P (100 + 15/100)
⇒ $7820 = P × 115/100
⇒ P × 115/100 = $7820
⇒ P = 7820/115/100
⇒ P = 7820 × 100/115
⇒ P = 7820 × 100/115
⇒ P = 782000/115
⇒ P = $6800
Thus, the sum borrowed (P) = $6800 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 7820, then the Principal = 100/115 × 7820
= 100 × 7820/115
= 782000/115
= 6800
Thus, Principal = $6800
Thus, the sum borrowed = $6800 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
(2) Joshua had to pay $5341 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) How much loan did Charles borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7080 to clear it?
(4) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(5) Charles had to pay $4134 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.
(7) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.
(8) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 5% simple interest?
(9) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 4 years.
(10) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.