Question:
Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.
Correct Answer
$10498
Solution And Explanation
Solution
Given,
Principal (P) = $5800
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) = $5800 × 9% × 9
= $5800 ×9/100 × 9
= 5800 × 9 × 9/100
= 52200 × 9/100
= 469800/100
= $4698
Thus, Simple Interest = $4698
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 = $5800 + $4698
= $10498
Thus, Amount to be paid = $10498 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 = $5800
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 9 years
Thus, Amount (A)
= $5800 + ($5800 × 9% × 9)
= $5800 + ($5800 ×9/100 × 9)
= $5800 + (5800 × 9 × 9/100)
= $5800 + (52200 × 9/100)
= $5800 + (469800/100)
= $5800 + $4698 = $10498
Thus, Amount (A) to be paid = $10498 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 $5800, the simple interest in 1 year
= 9/100 × 5800
= 9 × 5800/100
= 52200/100 = $522
Thus, simple interest for 1 year = $522
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $522 × 9 = $4698
Thus, Simple Interest (SI) = $4698
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $4698
= $10498
Thus, Amount to be paid = $10498 Answer
Similar Questions
(1) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.
(2) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 4 years.
(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 7 years.
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.
(6) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 3 years.
(8) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.
(9) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(10) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.