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) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 3 years.
(2) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8312.5 to clear it?
(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 7 years.
(4) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 3 years.
(6) Emily had to pay $5320 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 4 years.
(8) If David paid $4080 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 7% simple interest?
(10) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.