Question:
Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 8% simple interest.
Correct Answer
$9720
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 8%
Time (t) = 10 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% × 10
= $5400 ×8/100 × 10
= 5400 × 8 × 10/100
= 43200 × 10/100
= 432000/100
= $4320
Thus, Simple Interest = $4320
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 + $4320
= $9720
Thus, Amount to be paid = $9720 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) = 10 years
Thus, Amount (A)
= $5400 + ($5400 × 8% × 10)
= $5400 + ($5400 ×8/100 × 10)
= $5400 + (5400 × 8 × 10/100)
= $5400 + (43200 × 10/100)
= $5400 + (432000/100)
= $5400 + $4320 = $9720
Thus, Amount (A) to be paid = $9720 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 10 years
= Simple interest for 1 year × 10
= $432 × 10 = $4320
Thus, Simple Interest (SI) = $4320
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $4320
= $9720
Thus, Amount to be paid = $9720 Answer
Similar Questions
(1) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 6% simple interest?
(2) If Donald paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 8 years.
(4) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?
(5) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.
(7) If Daniel paid $4592 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) If Andrew paid $5568 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.
(10) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.