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) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 8 years.
(2) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 5% simple interest?
(3) If Robert borrowed $3100 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 5% simple interest?
(5) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(6) Donald had to pay $4770 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) If Robert paid $3720 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.
(9) In how much time a principal of $3100 will amount to $3596 at a simple interest of 4% per annum?
(10) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.