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) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(2) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 3 years.
(4) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 2% simple interest?
(5) Emily had to pay $5035 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Karen had to pay $4305.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(8) How much loan did Steven borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8250 to clear it?
(9) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.