Question:
Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.
Correct Answer
$10136
Solution And Explanation
Solution
Given,
Principal (P) = $5600
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) = $5600 × 9% × 9
= $5600 ×9/100 × 9
= 5600 × 9 × 9/100
= 50400 × 9/100
= 453600/100
= $4536
Thus, Simple Interest = $4536
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 = $5600 + $4536
= $10136
Thus, Amount to be paid = $10136 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 = $5600
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 9 years
Thus, Amount (A)
= $5600 + ($5600 × 9% × 9)
= $5600 + ($5600 ×9/100 × 9)
= $5600 + (5600 × 9 × 9/100)
= $5600 + (50400 × 9/100)
= $5600 + (453600/100)
= $5600 + $4536 = $10136
Thus, Amount (A) to be paid = $10136 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 $5600, the simple interest in 1 year
= 9/100 × 5600
= 9 × 5600/100
= 50400/100 = $504
Thus, simple interest for 1 year = $504
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $504 × 9 = $4536
Thus, Simple Interest (SI) = $4536
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $4536
= $10136
Thus, Amount to be paid = $10136 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.
(3) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(4) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 8% simple interest?
(6) How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?
(7) Nancy had to pay $4523.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) If Betty paid $4760 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) How much loan did Deborah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8195 to clear it?
(10) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 5% simple interest?