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 if Jennifer borrowed a sum of $3250 at 6% simple interest for 4 years.
(2) If Jennifer borrowed $3250 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(3) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.
(4) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(5) Andrew had to pay $5376 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.
(9) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.
(10) How much loan did Susan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6215 to clear it?