Question:
Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 8 years.
Correct Answer
$8600
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 9%
Time (t) = 8 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% × 8
= $5000 ×9/100 × 8
= 5000 × 9 × 8/100
= 45000 × 8/100
= 360000/100
= $3600
Thus, Simple Interest = $3600
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 + $3600
= $8600
Thus, Amount to be paid = $8600 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) = 8 years
Thus, Amount (A)
= $5000 + ($5000 × 9% × 8)
= $5000 + ($5000 ×9/100 × 8)
= $5000 + (5000 × 9 × 8/100)
= $5000 + (45000 × 8/100)
= $5000 + (360000/100)
= $5000 + $3600 = $8600
Thus, Amount (A) to be paid = $8600 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 8 years
= Simple interest for 1 year × 8
= $450 × 8 = $3600
Thus, Simple Interest (SI) = $3600
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $3600
= $8600
Thus, Amount to be paid = $8600 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.
(2) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?
(3) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
(5) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 4 years.
(7) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 4 years.
(8) Mark had to pay $4664 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.
(10) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.