Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.
Correct Answer
$6786
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 2%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 8
= $5850 ×2/100 × 8
= 5850 × 2 × 8/100
= 11700 × 8/100
= 93600/100
= $936
Thus, Simple Interest = $936
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 + $936
= $6786
Thus, Amount to be paid = $6786 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) = 2%
And, Time (t) = 8 years
Thus, Amount (A)
= $5850 + ($5850 × 2% × 8)
= $5850 + ($5850 ×2/100 × 8)
= $5850 + (5850 × 2 × 8/100)
= $5850 + (11700 × 8/100)
= $5850 + (93600/100)
= $5850 + $936 = $6786
Thus, Amount (A) to be paid = $6786 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5850, the simple interest in 1 year
= 2/100 × 5850
= 2 × 5850/100
= 11700/100 = $117
Thus, simple interest for 1 year = $117
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $117 × 8 = $936
Thus, Simple Interest (SI) = $936
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $936
= $6786
Thus, Amount to be paid = $6786 Answer
Similar Questions
(1) If Robert paid $3720 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9593 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.
(4) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 3 years.
(5) In how much time a principal of $3150 will amount to $3339 at a simple interest of 2% per annum?
(6) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3100 will amount to $3472 at a simple interest of 4% per annum?
(8) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.
(10) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.