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) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(2) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $9280 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 3% per annum?
(4) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.
(5) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7980 to clear it?
(6) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 4 years.
(7) Matthew had to pay $4704 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 4 years.
(9) If Mark paid $5104 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.