Question:
Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 8 years.
Correct Answer
$9460
Solution And Explanation
Solution
Given,
Principal (P) = $5500
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) = $5500 × 9% × 8
= $5500 ×9/100 × 8
= 5500 × 9 × 8/100
= 49500 × 8/100
= 396000/100
= $3960
Thus, Simple Interest = $3960
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 = $5500 + $3960
= $9460
Thus, Amount to be paid = $9460 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 = $5500
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5500 + ($5500 × 9% × 8)
= $5500 + ($5500 ×9/100 × 8)
= $5500 + (5500 × 9 × 8/100)
= $5500 + (49500 × 8/100)
= $5500 + (396000/100)
= $5500 + $3960 = $9460
Thus, Amount (A) to be paid = $9460 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 $5500, the simple interest in 1 year
= 9/100 × 5500
= 9 × 5500/100
= 49500/100 = $495
Thus, simple interest for 1 year = $495
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $495 × 8 = $3960
Thus, Simple Interest (SI) = $3960
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $3960
= $9460
Thus, Amount to be paid = $9460 Answer
Similar Questions
(1) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 8% simple interest?
(2) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7216 to clear the loan, then find the time period of the loan.
(3) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.
(5) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 5% simple interest?
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 7 years.
(7) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 3 years.
(9) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.
(10) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 3% simple interest.