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) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 8% simple interest?
(2) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
(3) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.
(4) How much loan did Christopher borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6600 to clear it?
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.
(6) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(7) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6556 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.
(9) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8337.5 to clear it?
(10) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 9% simple interest.