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) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 3 years.
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 4 years.
(3) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.
(4) What amount does David have to pay after 5 years if he takes a loan of $3400 at 4% simple interest?
(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 7 years.
(6) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(8) In how much time a principal of $3100 will amount to $3875 at a simple interest of 5% per annum?
(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 5% simple interest?
(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.