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) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 7 years.
(3) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 3 years.
(4) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(5) Betty had to pay $4505 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 9% simple interest?
(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.
(8) How much loan did Matthew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7750 to clear it?
(9) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 10% simple interest?
(10) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?