Question:
What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?
Correct Answer
$3520
Solution And Explanation
Solution
Given,
Principal (P) = $3200
Rate of Simple Interest (SI) = 5%
Time (t) = 2 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 2
= $3200 ×5/100 × 2
= 3200 × 5 × 2/100
= 16000 × 2/100
= 32000/100
= $320
Thus, Simple Interest = $320
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 + $320
= $3520
Thus, Amount to be paid = $3520 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) = 5%
And, Time (t) = 2 years
Thus, Amount (A)
= $3200 + ($3200 × 5% × 2)
= $3200 + ($3200 ×5/100 × 2)
= $3200 + (3200 × 5 × 2/100)
= $3200 + (16000 × 2/100)
= $3200 + (32000/100)
= $3200 + $320 = $3520
Thus, Amount (A) to be paid = $3520 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3200, the simple interest in 1 year
= 5/100 × 3200
= 5 × 3200/100
= 16000/100 = $160
Thus, simple interest for 1 year = $160
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $160 × 2 = $320
Thus, Simple Interest (SI) = $320
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3200 + $320
= $3520
Thus, Amount to be paid = $3520 Answer
Similar Questions
(1) If Michelle paid $5346 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Margaret had to pay $4741.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 7 years.
(4) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9350 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 8% simple interest for 7 years.
(6) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 8 years.
(8) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
(9) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?
(10) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.