Question:
Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.
Correct Answer
$10860
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 9%
Time (t) = 9 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) = $6000 × 9% × 9
= $6000 ×9/100 × 9
= 6000 × 9 × 9/100
= 54000 × 9/100
= 486000/100
= $4860
Thus, Simple Interest = $4860
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 = $6000 + $4860
= $10860
Thus, Amount to be paid = $10860 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 = $6000
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 9 years
Thus, Amount (A)
= $6000 + ($6000 × 9% × 9)
= $6000 + ($6000 ×9/100 × 9)
= $6000 + (6000 × 9 × 9/100)
= $6000 + (54000 × 9/100)
= $6000 + (486000/100)
= $6000 + $4860 = $10860
Thus, Amount (A) to be paid = $10860 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 $6000, the simple interest in 1 year
= 9/100 × 6000
= 9 × 6000/100
= 54000/100 = $540
Thus, simple interest for 1 year = $540
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $540 × 9 = $4860
Thus, Simple Interest (SI) = $4860
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $4860
= $10860
Thus, Amount to be paid = $10860 Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 4 years.
(2) Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?
(5) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?
(6) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.
(8) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 7 years.
(10) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 4 years.