Question:
Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
Correct Answer
$9500
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 10%
Time (t) = 9 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% × 9
= $5000 ×10/100 × 9
= 5000 × 10 × 9/100
= 50000 × 9/100
= 450000/100
= $4500
Thus, Simple Interest = $4500
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 + $4500
= $9500
Thus, Amount to be paid = $9500 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) = 9 years
Thus, Amount (A)
= $5000 + ($5000 × 10% × 9)
= $5000 + ($5000 ×10/100 × 9)
= $5000 + (5000 × 10 × 9/100)
= $5000 + (50000 × 9/100)
= $5000 + (450000/100)
= $5000 + $4500 = $9500
Thus, Amount (A) to be paid = $9500 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 9 years
= Simple interest for 1 year × 9
= $500 × 9 = $4500
Thus, Simple Interest (SI) = $4500
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $4500
= $9500
Thus, Amount to be paid = $9500 Answer
Similar Questions
(1) If Thomas paid $4408 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9955 to clear the loan, then find the time period of the loan.
(3) How much loan did Ronald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9375 to clear it?
(4) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
(5) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(6) If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 7 years.
(8) If Elizabeth paid $3726 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) If Patricia paid $3528 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 3 years.