Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 8 years.
Correct Answer
$8658
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 6%
Time (t) = 8 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) = $5850 × 6% × 8
= $5850 ×6/100 × 8
= 5850 × 6 × 8/100
= 35100 × 8/100
= 280800/100
= $2808
Thus, Simple Interest = $2808
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 = $5850 + $2808
= $8658
Thus, Amount to be paid = $8658 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 = $5850
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5850 + ($5850 × 6% × 8)
= $5850 + ($5850 ×6/100 × 8)
= $5850 + (5850 × 6 × 8/100)
= $5850 + (35100 × 8/100)
= $5850 + (280800/100)
= $5850 + $2808 = $8658
Thus, Amount (A) to be paid = $8658 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 $5850, the simple interest in 1 year
= 6/100 × 5850
= 6 × 5850/100
= 35100/100 = $351
Thus, simple interest for 1 year = $351
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $351 × 8 = $2808
Thus, Simple Interest (SI) = $2808
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $2808
= $8658
Thus, Amount to be paid = $8658 Answer
Similar Questions
(1) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 6% simple interest?
(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 8 years.
(3) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 4 years.
(5) Karen had to pay $4542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) If Jessica borrowed $3750 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 4 years.
(9) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.
(10) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.