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) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
(2) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 4 years.
(3) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.
(4) If Robert paid $3720 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) What amount will be due after 2 years if John borrowed a sum of $3100 at a 5% simple interest?
(6) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 7% simple interest?
(7) If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?
(9) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.
(10) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?