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) In how much time a principal of $3000 will amount to $3360 at a simple interest of 3% per annum?
(2) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $10498 to clear the loan, then find the time period of the loan.
(3) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 6% simple interest?
(4) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.
(5) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 3 years.
(6) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.
(7) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 6% simple interest?
(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 7 years.
(10) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.