Question:
Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.
Correct Answer
$6726
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 2%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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) = $5700 × 2% × 9
= $5700 ×2/100 × 9
= 5700 × 2 × 9/100
= 11400 × 9/100
= 102600/100
= $1026
Thus, Simple Interest = $1026
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 = $5700 + $1026
= $6726
Thus, Amount to be paid = $6726 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 = $5700
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 9 years
Thus, Amount (A)
= $5700 + ($5700 × 2% × 9)
= $5700 + ($5700 ×2/100 × 9)
= $5700 + (5700 × 2 × 9/100)
= $5700 + (11400 × 9/100)
= $5700 + (102600/100)
= $5700 + $1026 = $6726
Thus, Amount (A) to be paid = $6726 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5700, the simple interest in 1 year
= 2/100 × 5700
= 2 × 5700/100
= 11400/100 = $114
Thus, simple interest for 1 year = $114
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $114 × 9 = $1026
Thus, Simple Interest (SI) = $1026
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $1026
= $6726
Thus, Amount to be paid = $6726 Answer
Similar Questions
(1) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.
(3) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11800 to clear the loan, then find the time period of the loan.
(4) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6300 to clear it?
(5) If Michael borrowed $3300 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(6) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 9% simple interest.
(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.
(8) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?
(10) In how much time a principal of $3150 will amount to $3937.5 at a simple interest of 5% per annum?