Question:
Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
Correct Answer
$9683.5
Solution And Explanation
Solution
Given,
Principal (P) = $5350
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) = $5350 × 9% × 9
= $5350 ×9/100 × 9
= 5350 × 9 × 9/100
= 48150 × 9/100
= 433350/100
= $4333.5
Thus, Simple Interest = $4333.5
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 = $5350 + $4333.5
= $9683.5
Thus, Amount to be paid = $9683.5 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 = $5350
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 9 years
Thus, Amount (A)
= $5350 + ($5350 × 9% × 9)
= $5350 + ($5350 ×9/100 × 9)
= $5350 + (5350 × 9 × 9/100)
= $5350 + (48150 × 9/100)
= $5350 + (433350/100)
= $5350 + $4333.5 = $9683.5
Thus, Amount (A) to be paid = $9683.5 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 $5350, the simple interest in 1 year
= 9/100 × 5350
= 9 × 5350/100
= 48150/100 = $481.5
Thus, simple interest for 1 year = $481.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $481.5 × 9 = $4333.5
Thus, Simple Interest (SI) = $4333.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $4333.5
= $9683.5
Thus, Amount to be paid = $9683.5 Answer
Similar Questions
(1) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.
(2) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 3 years.
(4) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.
(5) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8940 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.
(7) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 3 years.
(9) Michelle had to pay $5247 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 7 years.