Question:
Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.
Correct Answer
$11115
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 9%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 10
= $5850 ×9/100 × 10
= 5850 × 9 × 10/100
= 52650 × 10/100
= 526500/100
= $5265
Thus, Simple Interest = $5265
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 + $5265
= $11115
Thus, Amount to be paid = $11115 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) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5850 + ($5850 × 9% × 10)
= $5850 + ($5850 ×9/100 × 10)
= $5850 + (5850 × 9 × 10/100)
= $5850 + (52650 × 10/100)
= $5850 + (526500/100)
= $5850 + $5265 = $11115
Thus, Amount (A) to be paid = $11115 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5850, the simple interest in 1 year
= 9/100 × 5850
= 9 × 5850/100
= 52650/100 = $526.5
Thus, simple interest for 1 year = $526.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $526.5 × 10 = $5265
Thus, Simple Interest (SI) = $5265
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $5265
= $11115
Thus, Amount to be paid = $11115 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.
(2) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 8 years.
(4) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 8 years.
(6) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 7% simple interest?
(7) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 7 years.
(9) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 7% simple interest?
(10) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 3 years.