Question:
Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
Correct Answer
$9140.5
Solution And Explanation
Solution
Given,
Principal (P) = $5050
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) = $5050 × 9% × 9
= $5050 ×9/100 × 9
= 5050 × 9 × 9/100
= 45450 × 9/100
= 409050/100
= $4090.5
Thus, Simple Interest = $4090.5
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 = $5050 + $4090.5
= $9140.5
Thus, Amount to be paid = $9140.5 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 = $5050
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 9 years
Thus, Amount (A)
= $5050 + ($5050 × 9% × 9)
= $5050 + ($5050 ×9/100 × 9)
= $5050 + (5050 × 9 × 9/100)
= $5050 + (45450 × 9/100)
= $5050 + (409050/100)
= $5050 + $4090.5 = $9140.5
Thus, Amount (A) to be paid = $9140.5 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 $5050, the simple interest in 1 year
= 9/100 × 5050
= 9 × 5050/100
= 45450/100 = $454.5
Thus, simple interest for 1 year = $454.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $454.5 × 9 = $4090.5
Thus, Simple Interest (SI) = $4090.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $4090.5
= $9140.5
Thus, Amount to be paid = $9140.5 Answer
Similar Questions
(1) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(2) If Joseph borrowed $3700 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(3) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 3 years.
(4) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.
(5) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?
(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 7 years.
(7) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(8) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 2% simple interest?
(9) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?
(10) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 4% simple interest?