Question:
Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
Correct Answer
$10450
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 9%
Time (t) = 10 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) = $5500 × 9% × 10
= $5500 ×9/100 × 10
= 5500 × 9 × 10/100
= 49500 × 10/100
= 495000/100
= $4950
Thus, Simple Interest = $4950
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 + $4950
= $10450
Thus, Amount to be paid = $10450 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) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5500 + ($5500 × 9% × 10)
= $5500 + ($5500 ×9/100 × 10)
= $5500 + (5500 × 9 × 10/100)
= $5500 + (49500 × 10/100)
= $5500 + (495000/100)
= $5500 + $4950 = $10450
Thus, Amount (A) to be paid = $10450 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 $5500, the simple interest in 1 year
= 9/100 × 5500
= 9 × 5500/100
= 49500/100 = $495
Thus, simple interest for 1 year = $495
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $495 × 10 = $4950
Thus, Simple Interest (SI) = $4950
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $4950
= $10450
Thus, Amount to be paid = $10450 Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 7 years.
(3) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% simple interest?
(4) How much loan did Joshua borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8280 to clear it?
(5) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 8% simple interest?
(7) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(8) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?
(10) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 8 years.