Question:
Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.
Correct Answer
$9804
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 8%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 9
= $5700 ×8/100 × 9
= 5700 × 8 × 9/100
= 45600 × 9/100
= 410400/100
= $4104
Thus, Simple Interest = $4104
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 + $4104
= $9804
Thus, Amount to be paid = $9804 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) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5700 + ($5700 × 8% × 9)
= $5700 + ($5700 ×8/100 × 9)
= $5700 + (5700 × 8 × 9/100)
= $5700 + (45600 × 9/100)
= $5700 + (410400/100)
= $5700 + $4104 = $9804
Thus, Amount (A) to be paid = $9804 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5700, the simple interest in 1 year
= 8/100 × 5700
= 8 × 5700/100
= 45600/100 = $456
Thus, simple interest for 1 year = $456
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $456 × 9 = $4104
Thus, Simple Interest (SI) = $4104
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $4104
= $9804
Thus, Amount to be paid = $9804 Answer
Similar Questions
(1) How much loan did Edward borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8740 to clear it?
(2) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 4% simple interest?
(4) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(5) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(6) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.
(7) If William paid $3920 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) Andrew had to pay $5376 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.
(10) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.