Question:
Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.
Correct Answer
$7777
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 6%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 9
= $5050 ×6/100 × 9
= 5050 × 6 × 9/100
= 30300 × 9/100
= 272700/100
= $2727
Thus, Simple Interest = $2727
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 + $2727
= $7777
Thus, Amount to be paid = $7777 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) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5050 + ($5050 × 6% × 9)
= $5050 + ($5050 ×6/100 × 9)
= $5050 + (5050 × 6 × 9/100)
= $5050 + (30300 × 9/100)
= $5050 + (272700/100)
= $5050 + $2727 = $7777
Thus, Amount (A) to be paid = $7777 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5050, the simple interest in 1 year
= 6/100 × 5050
= 6 × 5050/100
= 30300/100 = $303
Thus, simple interest for 1 year = $303
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $303 × 9 = $2727
Thus, Simple Interest (SI) = $2727
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $2727
= $7777
Thus, Amount to be paid = $7777 Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.
(3) What amount does James have to pay after 6 years if he takes a loan of $3000 at 7% simple interest?
(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.
(5) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 4 years.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 8 years.
(7) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.
(8) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(9) 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.
(10) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.