Question:
Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 8% simple interest.
Correct Answer
$9460
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 8%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 9
= $5500 ×8/100 × 9
= 5500 × 8 × 9/100
= 44000 × 9/100
= 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) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5500 + ($5500 × 8% × 9)
= $5500 + ($5500 ×8/100 × 9)
= $5500 + (5500 × 8 × 9/100)
= $5500 + (44000 × 9/100)
= $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 = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5500, the simple interest in 1 year
= 8/100 × 5500
= 8 × 5500/100
= 44000/100 = $440
Thus, simple interest for 1 year = $440
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $440 × 9 = $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) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.
(2) Margaret had to pay $5002.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Lisa had to pay $4657.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) How much loan did Michelle borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7645 to clear it?
(5) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.
(7) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.
(8) Barbara had to pay $3976 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
(10) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.