Question:
Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.
Correct Answer
$10226.5
Solution And Explanation
Solution
Given,
Principal (P) = $5650
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) = $5650 × 9% × 9
= $5650 ×9/100 × 9
= 5650 × 9 × 9/100
= 50850 × 9/100
= 457650/100
= $4576.5
Thus, Simple Interest = $4576.5
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 = $5650 + $4576.5
= $10226.5
Thus, Amount to be paid = $10226.5 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 = $5650
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 9 years
Thus, Amount (A)
= $5650 + ($5650 × 9% × 9)
= $5650 + ($5650 ×9/100 × 9)
= $5650 + (5650 × 9 × 9/100)
= $5650 + (50850 × 9/100)
= $5650 + (457650/100)
= $5650 + $4576.5 = $10226.5
Thus, Amount (A) to be paid = $10226.5 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 $5650, the simple interest in 1 year
= 9/100 × 5650
= 9 × 5650/100
= 50850/100 = $508.5
Thus, simple interest for 1 year = $508.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $508.5 × 9 = $4576.5
Thus, Simple Interest (SI) = $4576.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $4576.5
= $10226.5
Thus, Amount to be paid = $10226.5 Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(2) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.
(4) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.
(5) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 3 years.
(7) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?
(8) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8692 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if William borrowed a sum of $3250 at a 10% simple interest?
(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 7 years.