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) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?
(2) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% simple interest?
(3) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.
(4) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 5% simple interest?
(5) If Steven paid $5152 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(7) How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?
(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.
(9) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.