Question:
Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
Correct Answer
$9955
Solution And Explanation
Solution
Given,
Principal (P) = $5500
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) = $5500 × 9% × 9
= $5500 ×9/100 × 9
= 5500 × 9 × 9/100
= 49500 × 9/100
= 445500/100
= $4455
Thus, Simple Interest = $4455
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 + $4455
= $9955
Thus, Amount to be paid = $9955 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) = 9 years
Thus, Amount (A)
= $5500 + ($5500 × 9% × 9)
= $5500 + ($5500 ×9/100 × 9)
= $5500 + (5500 × 9 × 9/100)
= $5500 + (49500 × 9/100)
= $5500 + (445500/100)
= $5500 + $4455 = $9955
Thus, Amount (A) to be paid = $9955 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 9 years
= Simple interest for 1 year × 9
= $495 × 9 = $4455
Thus, Simple Interest (SI) = $4455
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $4455
= $9955
Thus, Amount to be paid = $9955 Answer
Similar Questions
(1) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 4 years.
(2) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 7% simple interest?
(3) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 6% simple interest?
(4) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?
(5) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 4 years.
(7) If Robert borrowed $3100 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(8) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11222 to clear the loan, then find the time period of the loan.
(9) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.
(10) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.