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) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(2) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.
(3) What amount does John have to pay after 6 years if he takes a loan of $3200 at 9% simple interest?
(4) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 10% simple interest?
(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 8 years.
(6) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 10% simple interest?
(7) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.
(8) How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 8 years.
(10) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?