Question:
Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
Correct Answer
$10450
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 9%
Time (t) = 10 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) = $5500 × 9% × 10
= $5500 ×9/100 × 10
= 5500 × 9 × 10/100
= 49500 × 10/100
= 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) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5500 + ($5500 × 9% × 10)
= $5500 + ($5500 ×9/100 × 10)
= $5500 + (5500 × 9 × 10/100)
= $5500 + (49500 × 10/100)
= $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 = 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 $5500, the simple interest in 1 year
= 9/100 × 5500
= 9 × 5500/100
= 49500/100 = $495
Thus, simple interest for 1 year = $495
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $495 × 10 = $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) If Elizabeth paid $4002 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(4) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 4 years.
(5) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.
(6) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.
(7) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.
(8) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.
(9) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9676 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.