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) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?
(2) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 4 years.
(3) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 5% simple interest?
(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 7 years.
(5) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.
(6) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(7) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.
(8) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 4 years.
(10) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 9% simple interest?