Question:
Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.
Correct Answer
$10317
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 9%
Time (t) = 9 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% × 9
= $5700 ×9/100 × 9
= 5700 × 9 × 9/100
= 51300 × 9/100
= 461700/100
= $4617
Thus, Simple Interest = $4617
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 + $4617
= $10317
Thus, Amount to be paid = $10317 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) = 9 years
Thus, Amount (A)
= $5700 + ($5700 × 9% × 9)
= $5700 + ($5700 ×9/100 × 9)
= $5700 + (5700 × 9 × 9/100)
= $5700 + (51300 × 9/100)
= $5700 + (461700/100)
= $5700 + $4617 = $10317
Thus, Amount (A) to be paid = $10317 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 9 years
= Simple interest for 1 year × 9
= $513 × 9 = $4617
Thus, Simple Interest (SI) = $4617
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $4617
= $10317
Thus, Amount to be paid = $10317 Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.
(3) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.
(4) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?
(5) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.
(6) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9685 to clear the loan, then find the time period of the loan.
(7) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10660 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.
(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.
(10) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.