Question:
Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.
Correct Answer
$10830
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 9%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 10
= $5700 ×9/100 × 10
= 5700 × 9 × 10/100
= 51300 × 10/100
= 513000/100
= $5130
Thus, Simple Interest = $5130
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 + $5130
= $10830
Thus, Amount to be paid = $10830 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) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5700 + ($5700 × 9% × 10)
= $5700 + ($5700 ×9/100 × 10)
= $5700 + (5700 × 9 × 10/100)
= $5700 + (51300 × 10/100)
= $5700 + (513000/100)
= $5700 + $5130 = $10830
Thus, Amount (A) to be paid = $10830 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5700, the simple interest in 1 year
= 9/100 × 5700
= 9 × 5700/100
= 51300/100 = $513
Thus, simple interest for 1 year = $513
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $513 × 10 = $5130
Thus, Simple Interest (SI) = $5130
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $5130
= $10830
Thus, Amount to be paid = $10830 Answer
Similar Questions
(1) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 2% simple interest?
(2) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 5% simple interest?
(4) Nancy had to pay $4523.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?
(6) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.
(7) If Jennifer paid $3770 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 3 years.
(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 8 years.
(10) 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.