Question:
Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 8% simple interest.
Correct Answer
$9288
Solution And Explanation
Solution
Given,
Principal (P) = $5400
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) = $5400 × 8% × 9
= $5400 ×8/100 × 9
= 5400 × 8 × 9/100
= 43200 × 9/100
= 388800/100
= $3888
Thus, Simple Interest = $3888
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 + $3888
= $9288
Thus, Amount to be paid = $9288 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) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5400 + ($5400 × 8% × 9)
= $5400 + ($5400 ×8/100 × 9)
= $5400 + (5400 × 8 × 9/100)
= $5400 + (43200 × 9/100)
= $5400 + (388800/100)
= $5400 + $3888 = $9288
Thus, Amount (A) to be paid = $9288 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 $5400, the simple interest in 1 year
= 8/100 × 5400
= 8 × 5400/100
= 43200/100 = $432
Thus, simple interest for 1 year = $432
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $432 × 9 = $3888
Thus, Simple Interest (SI) = $3888
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $3888
= $9288
Thus, Amount to be paid = $9288 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.
(2) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.
(3) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8305 to clear it?
(4) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 7 years.
(6) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 8 years.
(7) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(9) What amount will be due after 2 years if James borrowed a sum of $3000 at a 9% simple interest?
(10) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.