Question:
Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.
Correct Answer
$5900
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 2%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 9
= $5000 ×2/100 × 9
= 5000 × 2 × 9/100
= 10000 × 9/100
= 90000/100
= $900
Thus, Simple Interest = $900
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 + $900
= $5900
Thus, Amount to be paid = $5900 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) = 2%
And, Time (t) = 9 years
Thus, Amount (A)
= $5000 + ($5000 × 2% × 9)
= $5000 + ($5000 ×2/100 × 9)
= $5000 + (5000 × 2 × 9/100)
= $5000 + (10000 × 9/100)
= $5000 + (90000/100)
= $5000 + $900 = $5900
Thus, Amount (A) to be paid = $5900 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5000, the simple interest in 1 year
= 2/100 × 5000
= 2 × 5000/100
= 10000/100 = $100
Thus, simple interest for 1 year = $100
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $100 × 9 = $900
Thus, Simple Interest (SI) = $900
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $900
= $5900
Thus, Amount to be paid = $5900 Answer
Similar Questions
(1) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) If Kenneth paid $5800 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) How much loan did Matthew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6820 to clear it?
(4) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.
(5) How much loan did Ryan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8690 to clear it?
(6) Paul had to pay $5405 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 8 years.
(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 3 years.
(10) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 3 years.