Question:
Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
Correct Answer
$10260
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 10%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $5400 × 10% × 9
= $5400 ×10/100 × 9
= 5400 × 10 × 9/100
= 54000 × 9/100
= 486000/100
= $4860
Thus, Simple Interest = $4860
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 = $5400 + $4860
= $10260
Thus, Amount to be paid = $10260 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 = $5400
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5400 + ($5400 × 10% × 9)
= $5400 + ($5400 ×10/100 × 9)
= $5400 + (5400 × 10 × 9/100)
= $5400 + (54000 × 9/100)
= $5400 + (486000/100)
= $5400 + $4860 = $10260
Thus, Amount (A) to be paid = $10260 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5400, the simple interest in 1 year
= 10/100 × 5400
= 10 × 5400/100
= 54000/100 = $540
Thus, simple interest for 1 year = $540
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $540 × 9 = $4860
Thus, Simple Interest (SI) = $4860
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $4860
= $10260
Thus, Amount to be paid = $10260 Answer
Similar Questions
(1) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 4 years.
(2) If Michelle paid $5544 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 4 years.
(4) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8797.5 to clear it?
(5) Jessica had to pay $4200 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) How much loan did Brian borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8640 to clear it?
(7) How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 8 years.
(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?
(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 3 years.