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) Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 7 years.
(4) What amount does John have to pay after 6 years if he takes a loan of $3200 at 7% simple interest?
(5) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.
(6) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 9% simple interest?
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 7 years.
(8) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 4 years.
(10) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.