Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 8 years.
Correct Answer
$9594
Solution And Explanation
Solution
Given,
Principal (P) = $5850
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) = $5850 × 8% × 8
= $5850 ×8/100 × 8
= 5850 × 8 × 8/100
= 46800 × 8/100
= 374400/100
= $3744
Thus, Simple Interest = $3744
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 + $3744
= $9594
Thus, Amount to be paid = $9594 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) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5850 + ($5850 × 8% × 8)
= $5850 + ($5850 ×8/100 × 8)
= $5850 + (5850 × 8 × 8/100)
= $5850 + (46800 × 8/100)
= $5850 + (374400/100)
= $5850 + $3744 = $9594
Thus, Amount (A) to be paid = $9594 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 $5850, the simple interest in 1 year
= 8/100 × 5850
= 8 × 5850/100
= 46800/100 = $468
Thus, simple interest for 1 year = $468
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $468 × 8 = $3744
Thus, Simple Interest (SI) = $3744
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $3744
= $9594
Thus, Amount to be paid = $9594 Answer
Similar Questions
(1) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 2% simple interest.
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.
(4) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 4 years.
(6) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 4 years.
(8) If Daniel paid $4428 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 3 years.
(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 8 years.