Question:
Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.
Correct Answer
$6785
Solution And Explanation
Solution
Given,
Principal (P) = $5750
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) = $5750 × 2% × 9
= $5750 ×2/100 × 9
= 5750 × 2 × 9/100
= 11500 × 9/100
= 103500/100
= $1035
Thus, Simple Interest = $1035
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 = $5750 + $1035
= $6785
Thus, Amount to be paid = $6785 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 = $5750
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 9 years
Thus, Amount (A)
= $5750 + ($5750 × 2% × 9)
= $5750 + ($5750 ×2/100 × 9)
= $5750 + (5750 × 2 × 9/100)
= $5750 + (11500 × 9/100)
= $5750 + (103500/100)
= $5750 + $1035 = $6785
Thus, Amount (A) to be paid = $6785 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 $5750, the simple interest in 1 year
= 2/100 × 5750
= 2 × 5750/100
= 11500/100 = $115
Thus, simple interest for 1 year = $115
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $115 × 9 = $1035
Thus, Simple Interest (SI) = $1035
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $1035
= $6785
Thus, Amount to be paid = $6785 Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.
(2) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?
(3) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(5) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?
(6) If Christopher borrowed $4000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(7) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 4 years.
(8) If Thomas paid $4560 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?
(10) How much loan did Jason borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8855 to clear it?