Question:
Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
Correct Answer
$9774
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 9%
Time (t) = 9 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) = $5400 × 9% × 9
= $5400 ×9/100 × 9
= 5400 × 9 × 9/100
= 48600 × 9/100
= 437400/100
= $4374
Thus, Simple Interest = $4374
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 + $4374
= $9774
Thus, Amount to be paid = $9774 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) = 9%
And, Time (t) = 9 years
Thus, Amount (A)
= $5400 + ($5400 × 9% × 9)
= $5400 + ($5400 ×9/100 × 9)
= $5400 + (5400 × 9 × 9/100)
= $5400 + (48600 × 9/100)
= $5400 + (437400/100)
= $5400 + $4374 = $9774
Thus, Amount (A) to be paid = $9774 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 $5400, the simple interest in 1 year
= 9/100 × 5400
= 9 × 5400/100
= 48600/100 = $486
Thus, simple interest for 1 year = $486
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $486 × 9 = $4374
Thus, Simple Interest (SI) = $4374
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $4374
= $9774
Thus, Amount to be paid = $9774 Answer
Similar Questions
(1) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 6% simple interest?
(2) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
(4) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 4 years.
(6) How much loan did Susan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6780 to clear it?
(7) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8296 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 4 years.
(9) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
(10) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 9% simple interest?