Question:
Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 8 years.
Correct Answer
$9840
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 8%
Time (t) = 8 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) = $6000 × 8% × 8
= $6000 ×8/100 × 8
= 6000 × 8 × 8/100
= 48000 × 8/100
= 384000/100
= $3840
Thus, Simple Interest = $3840
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 = $6000 + $3840
= $9840
Thus, Amount to be paid = $9840 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 = $6000
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $6000 + ($6000 × 8% × 8)
= $6000 + ($6000 ×8/100 × 8)
= $6000 + (6000 × 8 × 8/100)
= $6000 + (48000 × 8/100)
= $6000 + (384000/100)
= $6000 + $3840 = $9840
Thus, Amount (A) to be paid = $9840 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 $6000, the simple interest in 1 year
= 8/100 × 6000
= 8 × 6000/100
= 48000/100 = $480
Thus, simple interest for 1 year = $480
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $480 × 8 = $3840
Thus, Simple Interest (SI) = $3840
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $3840
= $9840
Thus, Amount to be paid = $9840 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.
(2) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.
(3) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 7 years.
(5) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6854 to clear the loan, then find the time period of the loan.
(6) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8791 to clear the loan, then find the time period of the loan.
(7) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 4 years.
(9) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 7% simple interest?
(10) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.