Question:
How much loan did Christopher borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6900 to clear it?
Correct Answer
$6000
Solution And Explanation
Solution
Given,
Amount (A) = $6900
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
$6900 = P (1 + 3% × 5)
⇒ $6900 = P (1 + 3/100 × 5)
⇒ $6900 = P (1 + 3 × 5/100)
⇒ $6900 = P (1 + 15/100)
⇒ $6900 = P (100 + 15/100)
⇒ $6900 = P × 115/100
⇒ P × 115/100 = $6900
⇒ P = 6900/115/100
⇒ P = 6900 × 100/115
⇒ P = 6900 × 100/115
⇒ P = 690000/115
⇒ P = $6000
Thus, the sum borrowed (P) = $6000 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 6900, then the Principal = 100/115 × 6900
= 100 × 6900/115
= 690000/115
= 6000
Thus, Principal = $6000
Thus, the sum borrowed = $6000 Answer
Similar Questions
(1) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 3 years.
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 3 years.
(3) 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.
(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?
(5) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 8 years.
(6) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(7) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?
(8) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?
(9) How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?
(10) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.