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) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 4 years.
(3) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(4) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.
(6) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(7) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.
(8) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?
(9) How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?
(10) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?