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) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?
(3) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(4) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(6) How much loan did Edward borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9120 to clear it?
(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.
(8) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(9) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 7 years.
(10) David had to pay $3604 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.