Question:
Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
Correct Answer
$10450
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 10%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $5500 × 10% × 9
= $5500 ×10/100 × 9
= 5500 × 10 × 9/100
= 55000 × 9/100
= 495000/100
= $4950
Thus, Simple Interest = $4950
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 = $5500 + $4950
= $10450
Thus, Amount to be paid = $10450 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 = $5500
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5500 + ($5500 × 10% × 9)
= $5500 + ($5500 ×10/100 × 9)
= $5500 + (5500 × 10 × 9/100)
= $5500 + (55000 × 9/100)
= $5500 + (495000/100)
= $5500 + $4950 = $10450
Thus, Amount (A) to be paid = $10450 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5500, the simple interest in 1 year
= 10/100 × 5500
= 10 × 5500/100
= 55000/100 = $550
Thus, simple interest for 1 year = $550
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $550 × 9 = $4950
Thus, Simple Interest (SI) = $4950
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $4950
= $10450
Thus, Amount to be paid = $10450 Answer
Similar Questions
(1) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11041 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 3 years.
(4) What amount does William have to pay after 6 years if he takes a loan of $3500 at 6% simple interest?
(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 3 years.
(6) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 3 years.
(7) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 4 years.
(9) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(10) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.