Question:
Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.
Correct Answer
$10045.5
Solution And Explanation
Solution
Given,
Principal (P) = $5550
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) = $5550 × 9% × 9
= $5550 ×9/100 × 9
= 5550 × 9 × 9/100
= 49950 × 9/100
= 449550/100
= $4495.5
Thus, Simple Interest = $4495.5
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 = $5550 + $4495.5
= $10045.5
Thus, Amount to be paid = $10045.5 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 = $5550
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 9 years
Thus, Amount (A)
= $5550 + ($5550 × 9% × 9)
= $5550 + ($5550 ×9/100 × 9)
= $5550 + (5550 × 9 × 9/100)
= $5550 + (49950 × 9/100)
= $5550 + (449550/100)
= $5550 + $4495.5 = $10045.5
Thus, Amount (A) to be paid = $10045.5 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 $5550, the simple interest in 1 year
= 9/100 × 5550
= 9 × 5550/100
= 49950/100 = $499.5
Thus, simple interest for 1 year = $499.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $499.5 × 9 = $4495.5
Thus, Simple Interest (SI) = $4495.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $4495.5
= $10045.5
Thus, Amount to be paid = $10045.5 Answer
Similar Questions
(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 7 years.
(2) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 3 years.
(4) Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 8 years.
(6) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 3 years.
(7) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.
(8) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 7% simple interest?
(9) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 9% simple interest.
(10) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.