Question:
Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.
Correct Answer
$8475
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 5%
Time (t) = 10 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) = $5650 × 5% × 10
= $5650 ×5/100 × 10
= 5650 × 5 × 10/100
= 28250 × 10/100
= 282500/100
= $2825
Thus, Simple Interest = $2825
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 + $2825
= $8475
Thus, Amount to be paid = $8475 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) = 5%
And, Time (t) = 10 years
Thus, Amount (A)
= $5650 + ($5650 × 5% × 10)
= $5650 + ($5650 ×5/100 × 10)
= $5650 + (5650 × 5 × 10/100)
= $5650 + (28250 × 10/100)
= $5650 + (282500/100)
= $5650 + $2825 = $8475
Thus, Amount (A) to be paid = $8475 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 $5650, the simple interest in 1 year
= 5/100 × 5650
= 5 × 5650/100
= 28250/100 = $282.5
Thus, simple interest for 1 year = $282.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $282.5 × 10 = $2825
Thus, Simple Interest (SI) = $2825
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $2825
= $8475
Thus, Amount to be paid = $8475 Answer
Similar Questions
(1) How much loan did Brian borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7920 to clear it?
(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 3 years.
(3) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.
(4) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.
(6) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(8) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?
(9) If Barbara paid $3976 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 10% simple interest.