Question:
Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 8 years.
Correct Answer
$10320
Solution And Explanation
Solution
Given,
Principal (P) = $6000
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) = $6000 × 9% × 8
= $6000 ×9/100 × 8
= 6000 × 9 × 8/100
= 54000 × 8/100
= 432000/100
= $4320
Thus, Simple Interest = $4320
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 + $4320
= $10320
Thus, Amount to be paid = $10320 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) = 8 years
Thus, Amount (A)
= $6000 + ($6000 × 9% × 8)
= $6000 + ($6000 ×9/100 × 8)
= $6000 + (6000 × 9 × 8/100)
= $6000 + (54000 × 8/100)
= $6000 + (432000/100)
= $6000 + $4320 = $10320
Thus, Amount (A) to be paid = $10320 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 8 years
= Simple interest for 1 year × 8
= $540 × 8 = $4320
Thus, Simple Interest (SI) = $4320
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $4320
= $10320
Thus, Amount to be paid = $10320 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
(2) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.
(3) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.
(4) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9348 to clear the loan, then find the time period of the loan.
(5) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.
(7) What amount will be due after 2 years if David borrowed a sum of $3200 at a 7% simple interest?
(8) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?
(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 4 years.
(10) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.