Question:
Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.
Correct Answer
$8772
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 8%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $5100 × 8% × 9
= $5100 ×8/100 × 9
= 5100 × 8 × 9/100
= 40800 × 9/100
= 367200/100
= $3672
Thus, Simple Interest = $3672
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 = $5100 + $3672
= $8772
Thus, Amount to be paid = $8772 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 = $5100
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5100 + ($5100 × 8% × 9)
= $5100 + ($5100 ×8/100 × 9)
= $5100 + (5100 × 8 × 9/100)
= $5100 + (40800 × 9/100)
= $5100 + (367200/100)
= $5100 + $3672 = $8772
Thus, Amount (A) to be paid = $8772 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5100, the simple interest in 1 year
= 8/100 × 5100
= 8 × 5100/100
= 40800/100 = $408
Thus, simple interest for 1 year = $408
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $408 × 9 = $3672
Thus, Simple Interest (SI) = $3672
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $3672
= $8772
Thus, Amount to be paid = $8772 Answer
Similar Questions
(1) What amount will be due after 2 years if James borrowed a sum of $3000 at a 4% simple interest?
(2) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 8% simple interest?
(3) If Lisa paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.
(5) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3000 will amount to $3360 at a simple interest of 4% per annum?
(7) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.
(8) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.
(9) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.
(10) If James paid $3480 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.