Question:
Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
Correct Answer
$10000
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 10%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5000 × 10% × 10
= $5000 ×10/100 × 10
= 5000 × 10 × 10/100
= 50000 × 10/100
= 500000/100
= $5000
Thus, Simple Interest = $5000
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $5000
= $10000
Thus, Amount to be paid = $10000 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5000
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 10 years
Thus, Amount (A)
= $5000 + ($5000 × 10% × 10)
= $5000 + ($5000 ×10/100 × 10)
= $5000 + (5000 × 10 × 10/100)
= $5000 + (50000 × 10/100)
= $5000 + (500000/100)
= $5000 + $5000 = $10000
Thus, Amount (A) to be paid = $10000 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5000, the simple interest in 1 year
= 10/100 × 5000
= 10 × 5000/100
= 50000/100 = $500
Thus, simple interest for 1 year = $500
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $500 × 10 = $5000
Thus, Simple Interest (SI) = $5000
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $5000
= $10000
Thus, Amount to be paid = $10000 Answer
Similar Questions
(1) If Joseph paid $4292 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 7 years.
(3) In how much time a principal of $3000 will amount to $3450 at a simple interest of 3% per annum?
(4) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.
(5) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?
(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 8 years.
(7) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.
(9) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 4 years.
(10) How much loan did Susan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6215 to clear it?