Question:
Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.
Correct Answer
$8400
Solution And Explanation
Solution
Given,
Principal (P) = $5600
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) = $5600 × 5% × 10
= $5600 ×5/100 × 10
= 5600 × 5 × 10/100
= 28000 × 10/100
= 280000/100
= $2800
Thus, Simple Interest = $2800
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 = $5600 + $2800
= $8400
Thus, Amount to be paid = $8400 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 = $5600
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 10 years
Thus, Amount (A)
= $5600 + ($5600 × 5% × 10)
= $5600 + ($5600 ×5/100 × 10)
= $5600 + (5600 × 5 × 10/100)
= $5600 + (28000 × 10/100)
= $5600 + (280000/100)
= $5600 + $2800 = $8400
Thus, Amount (A) to be paid = $8400 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 $5600, the simple interest in 1 year
= 5/100 × 5600
= 5 × 5600/100
= 28000/100 = $280
Thus, simple interest for 1 year = $280
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $280 × 10 = $2800
Thus, Simple Interest (SI) = $2800
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $2800
= $8400
Thus, Amount to be paid = $8400 Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.
(2) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(3) How much loan did Amanda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8222.5 to clear it?
(4) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.
(5) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.
(6) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?
(7) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 8 years.
(9) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.
(10) How much loan did Robert borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6120 to clear it?