Question:
Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 7 years.
Correct Answer
$9209.5
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 9%
Time (t) = 7 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% × 7
= $5650 ×9/100 × 7
= 5650 × 9 × 7/100
= 50850 × 7/100
= 355950/100
= $3559.5
Thus, Simple Interest = $3559.5
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 + $3559.5
= $9209.5
Thus, Amount to be paid = $9209.5 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) = 7 years
Thus, Amount (A)
= $5650 + ($5650 × 9% × 7)
= $5650 + ($5650 ×9/100 × 7)
= $5650 + (5650 × 9 × 7/100)
= $5650 + (50850 × 7/100)
= $5650 + (355950/100)
= $5650 + $3559.5 = $9209.5
Thus, Amount (A) to be paid = $9209.5 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 7 years
= Simple interest for 1 year × 7
= $508.5 × 7 = $3559.5
Thus, Simple Interest (SI) = $3559.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $3559.5
= $9209.5
Thus, Amount to be paid = $9209.5 Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?
(2) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.
(3) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.
(4) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 8 years.
(6) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.
(7) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?
(8) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.
(9) If William paid $4060 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.