Question:
Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
Correct Answer
$9546
Solution And Explanation
Solution
Given,
Principal (P) = $5550
Rate of Simple Interest (SI) = 8%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 9
= $5550 ×8/100 × 9
= 5550 × 8 × 9/100
= 44400 × 9/100
= 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) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5550 + ($5550 × 8% × 9)
= $5550 + ($5550 ×8/100 × 9)
= $5550 + (5550 × 8 × 9/100)
= $5550 + (44400 × 9/100)
= $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 = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5550, the simple interest in 1 year
= 8/100 × 5550
= 8 × 5550/100
= 44400/100 = $444
Thus, simple interest for 1 year = $444
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $444 × 9 = $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) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(2) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 3 years.
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 3 years.
(4) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 10% simple interest?
(5) If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?
(7) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 4% simple interest?
(8) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(10) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?