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 after 10 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.
(2) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.
(3) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 3% simple interest?
(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 7 years.
(5) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 7 years.
(6) What amount does James have to pay after 6 years if he takes a loan of $3000 at 8% simple interest?
(7) What amount will be due after 2 years if James borrowed a sum of $3000 at a 4% simple interest?
(8) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?
(9) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(10) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 4% simple interest?