Question:
Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.
Correct Answer
$11020
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 10%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $5800 × 10% × 9
= $5800 ×10/100 × 9
= 5800 × 10 × 9/100
= 58000 × 9/100
= 522000/100
= $5220
Thus, Simple Interest = $5220
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 = $5800 + $5220
= $11020
Thus, Amount to be paid = $11020 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 = $5800
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5800 + ($5800 × 10% × 9)
= $5800 + ($5800 ×10/100 × 9)
= $5800 + (5800 × 10 × 9/100)
= $5800 + (58000 × 9/100)
= $5800 + (522000/100)
= $5800 + $5220 = $11020
Thus, Amount (A) to be paid = $11020 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5800, the simple interest in 1 year
= 10/100 × 5800
= 10 × 5800/100
= 58000/100 = $580
Thus, simple interest for 1 year = $580
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $580 × 9 = $5220
Thus, Simple Interest (SI) = $5220
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $5220
= $11020
Thus, Amount to be paid = $11020 Answer
Similar Questions
(1) Patricia had to pay $3622.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.
(3) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?
(5) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.
(6) What amount does John have to pay after 6 years if he takes a loan of $3200 at 4% simple interest?
(7) What amount does James have to pay after 5 years if he takes a loan of $3000 at 9% simple interest?
(8) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?
(10) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 8 years.