Question:
How much loan did Kenneth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7700 to clear it?
Correct Answer
$7000
Solution And Explanation
Solution
Given,
Amount (A) = $7700
Rate of Simple Interest (R) = 2%
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
$7700 = P (1 + 2% × 5)
⇒ $7700 = P (1 + 2/100 × 5)
⇒ $7700 = P (1 + 2 × 5/100)
⇒ $7700 = P (1 + 10/100)
⇒ $7700 = P (100 + 10/100)
⇒ $7700 = P × 110/100
⇒ P × 110/100 = $7700
⇒ P = 7700/110/100
⇒ P = 7700 × 100/110
⇒ P = 7700 × 100/110
⇒ P = 770000/110
⇒ P = $7000
Thus, the sum borrowed (P) = $7000 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 7700, then the Principal = 100/110 × 7700
= 100 × 7700/110
= 770000/110
= 7000
Thus, Principal = $7000
Thus, the sum borrowed = $7000 Answer
Similar Questions
(1) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 5% simple interest?
(2) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(3) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 2% simple interest?
(4) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 4 years.
(5) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?
(6) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 4% simple interest?
(8) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 3 years.
(9) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.
(10) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.