Question:
Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 8 years.
Correct Answer
$9288
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 9%
Time (t) = 8 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% × 8
= $5400 ×9/100 × 8
= 5400 × 9 × 8/100
= 48600 × 8/100
= 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) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5400 + ($5400 × 9% × 8)
= $5400 + ($5400 ×9/100 × 8)
= $5400 + (5400 × 9 × 8/100)
= $5400 + (48600 × 8/100)
= $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 = 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 8 years
= Simple interest for 1 year × 8
= $486 × 8 = $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) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 3 years.
(2) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?
(3) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(4) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(5) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?
(6) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.
(8) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 8 years.
(9) If Patricia borrowed $3150 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?