Question:
Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
Correct Answer
$10640
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (SI) = 10%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 9
= $5600 ×10/100 × 9
= 5600 × 10 × 9/100
= 56000 × 9/100
= 504000/100
= $5040
Thus, Simple Interest = $5040
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 + $5040
= $10640
Thus, Amount to be paid = $10640 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) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5600 + ($5600 × 10% × 9)
= $5600 + ($5600 ×10/100 × 9)
= $5600 + (5600 × 10 × 9/100)
= $5600 + (56000 × 9/100)
= $5600 + (504000/100)
= $5600 + $5040 = $10640
Thus, Amount (A) to be paid = $10640 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5600, the simple interest in 1 year
= 10/100 × 5600
= 10 × 5600/100
= 56000/100 = $560
Thus, simple interest for 1 year = $560
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $560 × 9 = $5040
Thus, Simple Interest (SI) = $5040
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $5040
= $10640
Thus, Amount to be paid = $10640 Answer
Similar Questions
(1) What amount does William have to pay after 6 years if he takes a loan of $3500 at 5% simple interest?
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 8 years.
(3) How much loan did Kevin borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8165 to clear it?
(4) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(5) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 4 years.
(7) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(8) How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?
(9) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 4 years.
(10) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?