Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 3 years.
Correct Answer
$4278
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 8%
Time (t) = 3 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) = $3450 × 8% × 3
= $3450 ×8/100 × 3
= 3450 × 8 × 3/100
= 27600 × 3/100
= 82800/100
= $828
Thus, Simple Interest = $828
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 = $3450 + $828
= $4278
Thus, Amount to be paid = $4278 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 = $3450
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 3 years
Thus, Amount (A)
= $3450 + ($3450 × 8% × 3)
= $3450 + ($3450 ×8/100 × 3)
= $3450 + (3450 × 8 × 3/100)
= $3450 + (27600 × 3/100)
= $3450 + (82800/100)
= $3450 + $828 = $4278
Thus, Amount (A) to be paid = $4278 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 $3450, the simple interest in 1 year
= 8/100 × 3450
= 8 × 3450/100
= 27600/100 = $276
Thus, simple interest for 1 year = $276
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $276 × 3 = $828
Thus, Simple Interest (SI) = $828
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $828
= $4278
Thus, Amount to be paid = $4278 Answer
Similar Questions
(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 3 years.
(2) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 4 years.
(4) What amount will be due after 2 years if John borrowed a sum of $3100 at a 6% simple interest?
(5) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 3 years.
(6) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?
(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.
(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.
(9) How much loan did Anthony borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7245 to clear it?
(10) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 4 years.