Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.
Correct Answer
$9804
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 9%
Time (t) = 8 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% × 8
= $5700 ×9/100 × 8
= 5700 × 9 × 8/100
= 51300 × 8/100
= 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) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5700 + ($5700 × 9% × 8)
= $5700 + ($5700 ×9/100 × 8)
= $5700 + (5700 × 9 × 8/100)
= $5700 + (51300 × 8/100)
= $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 = 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 8 years
= Simple interest for 1 year × 8
= $513 × 8 = $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) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
(2) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 8% simple interest?
(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 3 years.
(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 7 years.
(5) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(6) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 9% simple interest?
(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 3 years.
(8) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 2% simple interest?
(9) If Linda paid $4020 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.