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) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.
(2) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.
(3) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7003 to clear the loan, then find the time period of the loan.
(4) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 7% simple interest?
(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.
(6) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.
(7) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(8) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 2% simple interest?
(9) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 7 years.
(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 4 years.