Question:
Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
Correct Answer
$9595
Solution And Explanation
Solution
Given,
Principal (P) = $5050
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) = $5050 × 9% × 10
= $5050 ×9/100 × 10
= 5050 × 9 × 10/100
= 45450 × 10/100
= 454500/100
= $4545
Thus, Simple Interest = $4545
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 + $4545
= $9595
Thus, Amount to be paid = $9595 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) = 10 years
Thus, Amount (A)
= $5050 + ($5050 × 9% × 10)
= $5050 + ($5050 ×9/100 × 10)
= $5050 + (5050 × 9 × 10/100)
= $5050 + (45450 × 10/100)
= $5050 + (454500/100)
= $5050 + $4545 = $9595
Thus, Amount (A) to be paid = $9595 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 10 years
= Simple interest for 1 year × 10
= $454.5 × 10 = $4545
Thus, Simple Interest (SI) = $4545
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $4545
= $9595
Thus, Amount to be paid = $9595 Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.
(2) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 4 years.
(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 7 years.
(5) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.
(6) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
(7) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.
(8) How much loan did Donald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7475 to clear it?
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 7 years.
(10) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $6936 to clear the loan, then find the time period of the loan.