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) Michael had to pay $3696 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) How much loan did Susan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6497.5 to clear it?
(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 7 years.
(4) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 3 years.
(5) William had to pay $4025 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 8 years.
(8) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.
(9) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 4 years.
(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 7 years.