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) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 4 years.
(2) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.
(3) Linda had to pay $3651.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) In how much time a principal of $3000 will amount to $3240 at a simple interest of 4% per annum?
(5) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.
(6) If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 2% simple interest?
(8) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 3% simple interest.
(10) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.