Question:
Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.
Correct Answer
$11600
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 10%
Time (t) = 10 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% × 10
= $5800 ×10/100 × 10
= 5800 × 10 × 10/100
= 58000 × 10/100
= 580000/100
= $5800
Thus, Simple Interest = $5800
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 + $5800
= $11600
Thus, Amount to be paid = $11600 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) = 10 years
Thus, Amount (A)
= $5800 + ($5800 × 10% × 10)
= $5800 + ($5800 ×10/100 × 10)
= $5800 + (5800 × 10 × 10/100)
= $5800 + (58000 × 10/100)
= $5800 + (580000/100)
= $5800 + $5800 = $11600
Thus, Amount (A) to be paid = $11600 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 10 years
= Simple interest for 1 year × 10
= $580 × 10 = $5800
Thus, Simple Interest (SI) = $5800
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $5800
= $11600
Thus, Amount to be paid = $11600 Answer
Similar Questions
(1) John had to pay $3392 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7421 to clear the loan, then find the time period of the loan.
(3) How much loan did Anthony borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7245 to clear it?
(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 8 years.
(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 4 years.
(6) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.
(7) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.
(8) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(9) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?
(10) What amount does William have to pay after 5 years if he takes a loan of $3500 at 5% simple interest?