Question:
Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.
Correct Answer
$9890
Solution And Explanation
Solution
Given,
Principal (P) = $5750
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) = $5750 × 8% × 9
= $5750 ×8/100 × 9
= 5750 × 8 × 9/100
= 46000 × 9/100
= 414000/100
= $4140
Thus, Simple Interest = $4140
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 + $4140
= $9890
Thus, Amount to be paid = $9890 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) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5750 + ($5750 × 8% × 9)
= $5750 + ($5750 ×8/100 × 9)
= $5750 + (5750 × 8 × 9/100)
= $5750 + (46000 × 9/100)
= $5750 + (414000/100)
= $5750 + $4140 = $9890
Thus, Amount (A) to be paid = $9890 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 $5750, the simple interest in 1 year
= 8/100 × 5750
= 8 × 5750/100
= 46000/100 = $460
Thus, simple interest for 1 year = $460
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $460 × 9 = $4140
Thus, Simple Interest (SI) = $4140
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $4140
= $9890
Thus, Amount to be paid = $9890 Answer
Similar Questions
(1) If James borrowed $3000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 3 years.
(4) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.
(5) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(6) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?
(8) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 3 years.
(9) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
(10) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7072 to clear the loan, then find the time period of the loan.