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) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 3 years.
(2) How much loan did Thomas borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6960 to clear it?
(3) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.
(5) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(6) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.
(8) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.
(9) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(10) How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?