Question:
Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.
Correct Answer
$9535.5
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 7%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 9
= $5850 ×7/100 × 9
= 5850 × 7 × 9/100
= 40950 × 9/100
= 368550/100
= $3685.5
Thus, Simple Interest = $3685.5
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 + $3685.5
= $9535.5
Thus, Amount to be paid = $9535.5 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) = 7%
And, Time (t) = 9 years
Thus, Amount (A)
= $5850 + ($5850 × 7% × 9)
= $5850 + ($5850 ×7/100 × 9)
= $5850 + (5850 × 7 × 9/100)
= $5850 + (40950 × 9/100)
= $5850 + (368550/100)
= $5850 + $3685.5 = $9535.5
Thus, Amount (A) to be paid = $9535.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5850, the simple interest in 1 year
= 7/100 × 5850
= 7 × 5850/100
= 40950/100 = $409.5
Thus, simple interest for 1 year = $409.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $409.5 × 9 = $3685.5
Thus, Simple Interest (SI) = $3685.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $3685.5
= $9535.5
Thus, Amount to be paid = $9535.5 Answer
Similar Questions
(1) If Donald paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 8 years.
(4) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9348 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.
(6) 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.
(7) If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 9% simple interest?
(9) If Donna paid $5820 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 8 years.