Question:
Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 5% simple interest.
Correct Answer
$8100
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 5%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 10
= $5400 ×5/100 × 10
= 5400 × 5 × 10/100
= 27000 × 10/100
= 270000/100
= $2700
Thus, Simple Interest = $2700
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 + $2700
= $8100
Thus, Amount to be paid = $8100 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) = 5%
And, Time (t) = 10 years
Thus, Amount (A)
= $5400 + ($5400 × 5% × 10)
= $5400 + ($5400 ×5/100 × 10)
= $5400 + (5400 × 5 × 10/100)
= $5400 + (27000 × 10/100)
= $5400 + (270000/100)
= $5400 + $2700 = $8100
Thus, Amount (A) to be paid = $8100 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5400, the simple interest in 1 year
= 5/100 × 5400
= 5 × 5400/100
= 27000/100 = $270
Thus, simple interest for 1 year = $270
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $270 × 10 = $2700
Thus, Simple Interest (SI) = $2700
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $2700
= $8100
Thus, Amount to be paid = $8100 Answer
Similar Questions
(1) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 3 years.
(2) If Susan borrowed $3650 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 7 years.
(5) If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 7 years.
(7) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 7 years.
(8) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 4 years.
(9) What amount will be due after 2 years if William borrowed a sum of $3250 at a 7% simple interest?
(10) 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.