Question:
How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?
Correct Answer
$7400
Solution And Explanation
Solution
Given,
Amount (A) = $8140
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
$8140 = P (1 + 2% × 5)
⇒ $8140 = P (1 + 2/100 × 5)
⇒ $8140 = P (1 + 2 × 5/100)
⇒ $8140 = P (1 + 10/100)
⇒ $8140 = P (100 + 10/100)
⇒ $8140 = P × 110/100
⇒ P × 110/100 = $8140
⇒ P = 8140/110/100
⇒ P = 8140 × 100/110
⇒ P = 8140 × 100/110
⇒ P = 814000/110
⇒ P = $7400
Thus, the sum borrowed (P) = $7400 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 8140, then the Principal = 100/110 × 8140
= 100 × 8140/110
= 814000/110
= 7400
Thus, Principal = $7400
Thus, the sum borrowed = $7400 Answer
Similar Questions
(1) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(2) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.
(3) What amount does John have to pay after 6 years if he takes a loan of $3200 at 5% simple interest?
(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 4 years.
(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 4 years.
(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 8 years.
(7) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.
(9) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.
(10) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9060 to clear it?