Question:
What amount will be due after 2 years if David borrowed a sum of $3200 at a 9% simple interest?
Correct Answer
$3776
Solution And Explanation
Solution
Given,
Principal (P) = $3200
Rate of Simple Interest (SI) = 9%
Time (t) = 2 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) = $3200 × 9% × 2
= $3200 ×9/100 × 2
= 3200 × 9 × 2/100
= 28800 × 2/100
= 57600/100
= $576
Thus, Simple Interest = $576
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 = $3200 + $576
= $3776
Thus, Amount to be paid = $3776 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 = $3200
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 2 years
Thus, Amount (A)
= $3200 + ($3200 × 9% × 2)
= $3200 + ($3200 ×9/100 × 2)
= $3200 + (3200 × 9 × 2/100)
= $3200 + (28800 × 2/100)
= $3200 + (57600/100)
= $3200 + $576 = $3776
Thus, Amount (A) to be paid = $3776 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 $3200, the simple interest in 1 year
= 9/100 × 3200
= 9 × 3200/100
= 28800/100 = $288
Thus, simple interest for 1 year = $288
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $288 × 2 = $576
Thus, Simple Interest (SI) = $576
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3200 + $576
= $3776
Thus, Amount to be paid = $3776 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 7 years.
(3) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(4) If John paid $3584 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 5% simple interest?
(7) Karen had to pay $4187 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(9) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8869 to clear the loan, then find the time period of the loan.
(10) If Paul paid $5452 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.