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) How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?
(2) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 6% simple interest.
(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 2% simple interest?
(4) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 4 years.
(5) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.
(6) How much loan did James borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5500 to clear it?
(7) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.
(8) If Betty paid $5100 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.
(10) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.