Question:
Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
Correct Answer
$7480
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 4%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 9
= $5500 ×4/100 × 9
= 5500 × 4 × 9/100
= 22000 × 9/100
= 198000/100
= $1980
Thus, Simple Interest = $1980
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 + $1980
= $7480
Thus, Amount to be paid = $7480 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) = 4%
And, Time (t) = 9 years
Thus, Amount (A)
= $5500 + ($5500 × 4% × 9)
= $5500 + ($5500 ×4/100 × 9)
= $5500 + (5500 × 4 × 9/100)
= $5500 + (22000 × 9/100)
= $5500 + (198000/100)
= $5500 + $1980 = $7480
Thus, Amount (A) to be paid = $7480 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5500, the simple interest in 1 year
= 4/100 × 5500
= 4 × 5500/100
= 22000/100 = $220
Thus, simple interest for 1 year = $220
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $220 × 9 = $1980
Thus, Simple Interest (SI) = $1980
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $1980
= $7480
Thus, Amount to be paid = $7480 Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(2) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7897 to clear the loan, then find the time period of the loan.
(3) Michael had to pay $3597 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 7 years.
(5) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(7) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(8) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
(9) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 5% simple interest.