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) What amount does David have to pay after 6 years if he takes a loan of $3400 at 6% simple interest?
(2) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(3) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.
(5) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(6) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9360 to clear it?
(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 7 years.
(8) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(9) How much loan did Charles borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6490 to clear it?
(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 8 years.