Question:
Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.
Correct Answer
$11400
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 10%
Time (t) = 10 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) = $5700 × 10% × 10
= $5700 ×10/100 × 10
= 5700 × 10 × 10/100
= 57000 × 10/100
= 570000/100
= $5700
Thus, Simple Interest = $5700
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 = $5700 + $5700
= $11400
Thus, Amount to be paid = $11400 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 = $5700
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 10 years
Thus, Amount (A)
= $5700 + ($5700 × 10% × 10)
= $5700 + ($5700 ×10/100 × 10)
= $5700 + (5700 × 10 × 10/100)
= $5700 + (57000 × 10/100)
= $5700 + (570000/100)
= $5700 + $5700 = $11400
Thus, Amount (A) to be paid = $11400 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 $5700, the simple interest in 1 year
= 10/100 × 5700
= 10 × 5700/100
= 57000/100 = $570
Thus, simple interest for 1 year = $570
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $570 × 10 = $5700
Thus, Simple Interest (SI) = $5700
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $5700
= $11400
Thus, Amount to be paid = $11400 Answer
Similar Questions
(1) How much loan did Amanda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7865 to clear it?
(2) If James borrowed $3000 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 James borrowed a sum of $5000 at 3% simple interest for 8 years.
(4) How much loan did Brian borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7920 to clear it?
(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 8 years.
(6) How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?
(7) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 7% simple interest?
(8) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.
(9) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 8 years.