Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.
Correct Answer
$7254
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 8
= $5850 ×3/100 × 8
= 5850 × 3 × 8/100
= 17550 × 8/100
= 140400/100
= $1404
Thus, Simple Interest = $1404
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 + $1404
= $7254
Thus, Amount to be paid = $7254 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5850 + ($5850 × 3% × 8)
= $5850 + ($5850 ×3/100 × 8)
= $5850 + (5850 × 3 × 8/100)
= $5850 + (17550 × 8/100)
= $5850 + (140400/100)
= $5850 + $1404 = $7254
Thus, Amount (A) to be paid = $7254 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5850, the simple interest in 1 year
= 3/100 × 5850
= 3 × 5850/100
= 17550/100 = $175.5
Thus, simple interest for 1 year = $175.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $175.5 × 8 = $1404
Thus, Simple Interest (SI) = $1404
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $1404
= $7254
Thus, Amount to be paid = $7254 Answer
Similar Questions
(1) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 8 years.
(2) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?
(3) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?
(4) If Joseph paid $4292 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(6) How much loan did William borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6050 to clear it?
(7) How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?
(8) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.
(9) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 6% simple interest.