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) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(2) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 5% simple interest?
(3) How much loan did Charles borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6785 to clear it?
(4) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 2% simple interest?
(5) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.
(7) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.
(8) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 7 years.