Question:
Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.
Correct Answer
$9632
Solution And Explanation
Solution
Given,
Principal (P) = $5600
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) = $5600 × 9% × 8
= $5600 ×9/100 × 8
= 5600 × 9 × 8/100
= 50400 × 8/100
= 403200/100
= $4032
Thus, Simple Interest = $4032
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 + $4032
= $9632
Thus, Amount to be paid = $9632 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) = 8 years
Thus, Amount (A)
= $5600 + ($5600 × 9% × 8)
= $5600 + ($5600 ×9/100 × 8)
= $5600 + (5600 × 9 × 8/100)
= $5600 + (50400 × 8/100)
= $5600 + (403200/100)
= $5600 + $4032 = $9632
Thus, Amount (A) to be paid = $9632 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 8 years
= Simple interest for 1 year × 8
= $504 × 8 = $4032
Thus, Simple Interest (SI) = $4032
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $4032
= $9632
Thus, Amount to be paid = $9632 Answer
Similar Questions
(1) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% simple interest?
(2) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 4 years.
(3) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.
(4) Daniel had to pay $4346 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 4 years.
(7) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.
(8) How much loan did Ryan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9875 to clear it?
(9) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(10) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.