Question:
Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 5% simple interest.
Correct Answer
$8700
Solution And Explanation
Solution
Given,
Principal (P) = $5800
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) = $5800 × 5% × 10
= $5800 ×5/100 × 10
= 5800 × 5 × 10/100
= 29000 × 10/100
= 290000/100
= $2900
Thus, Simple Interest = $2900
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 + $2900
= $8700
Thus, Amount to be paid = $8700 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) = 5%
And, Time (t) = 10 years
Thus, Amount (A)
= $5800 + ($5800 × 5% × 10)
= $5800 + ($5800 ×5/100 × 10)
= $5800 + (5800 × 5 × 10/100)
= $5800 + (29000 × 10/100)
= $5800 + (290000/100)
= $5800 + $2900 = $8700
Thus, Amount (A) to be paid = $8700 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 $5800, the simple interest in 1 year
= 5/100 × 5800
= 5 × 5800/100
= 29000/100 = $290
Thus, simple interest for 1 year = $290
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $290 × 10 = $2900
Thus, Simple Interest (SI) = $2900
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $2900
= $8700
Thus, Amount to be paid = $8700 Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 4 years.
(3) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?
(4) In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 4 years.
(6) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 3 years.
(7) Elizabeth had to pay $3967.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Christopher had to pay $4480 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.