Question:
Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 8 years.
Correct Answer
$9546
Solution And Explanation
Solution
Given,
Principal (P) = $5550
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) = $5550 × 9% × 8
= $5550 ×9/100 × 8
= 5550 × 9 × 8/100
= 49950 × 8/100
= 399600/100
= $3996
Thus, Simple Interest = $3996
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 = $5550 + $3996
= $9546
Thus, Amount to be paid = $9546 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 = $5550
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5550 + ($5550 × 9% × 8)
= $5550 + ($5550 ×9/100 × 8)
= $5550 + (5550 × 9 × 8/100)
= $5550 + (49950 × 8/100)
= $5550 + (399600/100)
= $5550 + $3996 = $9546
Thus, Amount (A) to be paid = $9546 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 $5550, the simple interest in 1 year
= 9/100 × 5550
= 9 × 5550/100
= 49950/100 = $499.5
Thus, simple interest for 1 year = $499.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $499.5 × 8 = $3996
Thus, Simple Interest (SI) = $3996
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $3996
= $9546
Thus, Amount to be paid = $9546 Answer
Similar Questions
(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 7 years.
(2) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.
(3) In how much time a principal of $3050 will amount to $3233 at a simple interest of 2% per annum?
(4) If Paul paid $5264 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 2% simple interest?
(6) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 10% simple interest?
(7) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7599 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 8 years.
(9) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.
(10) How much loan did Matthew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7130 to clear it?