Question:
Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 9% simple interest.
Correct Answer
$9500
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 9%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 10
= $5000 ×9/100 × 10
= 5000 × 9 × 10/100
= 45000 × 10/100
= 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) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5000 + ($5000 × 9% × 10)
= $5000 + ($5000 ×9/100 × 10)
= $5000 + (5000 × 9 × 10/100)
= $5000 + (45000 × 10/100)
= $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 = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5000, the simple interest in 1 year
= 9/100 × 5000
= 9 × 5000/100
= 45000/100 = $450
Thus, simple interest for 1 year = $450
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $450 × 10 = $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) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.
(3) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 8 years.
(5) If Donald paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.
(7) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(8) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.
(9) Susan had to pay $4088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 8 years.