Question:
Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
Correct Answer
$11115
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 10%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 9
= $5850 ×10/100 × 9
= 5850 × 10 × 9/100
= 58500 × 9/100
= 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) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5850 + ($5850 × 10% × 9)
= $5850 + ($5850 ×10/100 × 9)
= $5850 + (5850 × 10 × 9/100)
= $5850 + (58500 × 9/100)
= $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 = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5850, the simple interest in 1 year
= 10/100 × 5850
= 10 × 5850/100
= 58500/100 = $585
Thus, simple interest for 1 year = $585
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $585 × 9 = $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) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(2) If Jessica borrowed $3750 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(3) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.
(4) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?
(5) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.
(6) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 8% simple interest?
(7) 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.
(8) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 3 years.
(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 8% simple interest?
(10) How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?