Question:
Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 8 years.
Correct Answer
$9718
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 9%
Time (t) = 8 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) = $5650 × 9% × 8
= $5650 ×9/100 × 8
= 5650 × 9 × 8/100
= 50850 × 8/100
= 406800/100
= $4068
Thus, Simple Interest = $4068
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 = $5650 + $4068
= $9718
Thus, Amount to be paid = $9718 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 = $5650
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5650 + ($5650 × 9% × 8)
= $5650 + ($5650 ×9/100 × 8)
= $5650 + (5650 × 9 × 8/100)
= $5650 + (50850 × 8/100)
= $5650 + (406800/100)
= $5650 + $4068 = $9718
Thus, Amount (A) to be paid = $9718 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 $5650, the simple interest in 1 year
= 9/100 × 5650
= 9 × 5650/100
= 50850/100 = $508.5
Thus, simple interest for 1 year = $508.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $508.5 × 8 = $4068
Thus, Simple Interest (SI) = $4068
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $4068
= $9718
Thus, Amount to be paid = $9718 Answer
Similar Questions
(1) How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?
(2) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
(3) In how much time a principal of $3050 will amount to $3416 at a simple interest of 3% per annum?
(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.
(5) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(6) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8750 to clear it?
(7) How much loan did Edward borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9120 to clear it?
(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.
(9) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.