Question:
Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.
Correct Answer
$10062
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 8%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 9
= $5850 ×8/100 × 9
= 5850 × 8 × 9/100
= 46800 × 9/100
= 421200/100
= $4212
Thus, Simple Interest = $4212
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 + $4212
= $10062
Thus, Amount to be paid = $10062 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) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5850 + ($5850 × 8% × 9)
= $5850 + ($5850 ×8/100 × 9)
= $5850 + (5850 × 8 × 9/100)
= $5850 + (46800 × 9/100)
= $5850 + (421200/100)
= $5850 + $4212 = $10062
Thus, Amount (A) to be paid = $10062 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5850, the simple interest in 1 year
= 8/100 × 5850
= 8 × 5850/100
= 46800/100 = $468
Thus, simple interest for 1 year = $468
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $468 × 9 = $4212
Thus, Simple Interest (SI) = $4212
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $4212
= $10062
Thus, Amount to be paid = $10062 Answer
Similar Questions
(1) How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?
(2) Ashley had to pay $5232.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?
(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 7 years.
(5) Mark had to pay $4664 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11316 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 8 years.
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 7 years.
(9) How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?
(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 8 years.