Question:
Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
Correct Answer
$8640
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 6%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 10
= $5400 ×6/100 × 10
= 5400 × 6 × 10/100
= 32400 × 10/100
= 324000/100
= $3240
Thus, Simple Interest = $3240
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 + $3240
= $8640
Thus, Amount to be paid = $8640 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) = 6%
And, Time (t) = 10 years
Thus, Amount (A)
= $5400 + ($5400 × 6% × 10)
= $5400 + ($5400 ×6/100 × 10)
= $5400 + (5400 × 6 × 10/100)
= $5400 + (32400 × 10/100)
= $5400 + (324000/100)
= $5400 + $3240 = $8640
Thus, Amount (A) to be paid = $8640 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5400, the simple interest in 1 year
= 6/100 × 5400
= 6 × 5400/100
= 32400/100 = $324
Thus, simple interest for 1 year = $324
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $324 × 10 = $3240
Thus, Simple Interest (SI) = $3240
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $3240
= $8640
Thus, Amount to be paid = $8640 Answer
Similar Questions
(1) Joshua had to pay $5194 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 3 years.
(3) Lisa had to pay $4536 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.
(5) Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 3 years.
(7) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.
(8) If Joseph paid $3996 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Patricia had to pay $3622.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.