Question:
Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.
Correct Answer
$8855
Solution And Explanation
Solution
Given,
Principal (P) = $5750
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) = $5750 × 6% × 9
= $5750 ×6/100 × 9
= 5750 × 6 × 9/100
= 34500 × 9/100
= 310500/100
= $3105
Thus, Simple Interest = $3105
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 + $3105
= $8855
Thus, Amount to be paid = $8855 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) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5750 + ($5750 × 6% × 9)
= $5750 + ($5750 ×6/100 × 9)
= $5750 + (5750 × 6 × 9/100)
= $5750 + (34500 × 9/100)
= $5750 + (310500/100)
= $5750 + $3105 = $8855
Thus, Amount (A) to be paid = $8855 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 $5750, the simple interest in 1 year
= 6/100 × 5750
= 6 × 5750/100
= 34500/100 = $345
Thus, simple interest for 1 year = $345
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $345 × 9 = $3105
Thus, Simple Interest (SI) = $3105
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $3105
= $8855
Thus, Amount to be paid = $8855 Answer
Similar Questions
(1) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 7% simple interest?
(2) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.
(3) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $13400 to clear the loan, then find the time period of the loan.
(4) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 3% simple interest?
(5) If Elizabeth paid $4002 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) Sandra had to pay $5117.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 7 years.
(8) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 3 years.
(9) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.
(10) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.