Question:
Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 8 years.
Correct Answer
$8120
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 5%
Time (t) = 8 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% × 8
= $5800 ×5/100 × 8
= 5800 × 5 × 8/100
= 29000 × 8/100
= 232000/100
= $2320
Thus, Simple Interest = $2320
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 + $2320
= $8120
Thus, Amount to be paid = $8120 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) = 8 years
Thus, Amount (A)
= $5800 + ($5800 × 5% × 8)
= $5800 + ($5800 ×5/100 × 8)
= $5800 + (5800 × 5 × 8/100)
= $5800 + (29000 × 8/100)
= $5800 + (232000/100)
= $5800 + $2320 = $8120
Thus, Amount (A) to be paid = $8120 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 8 years
= Simple interest for 1 year × 8
= $290 × 8 = $2320
Thus, Simple Interest (SI) = $2320
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $2320
= $8120
Thus, Amount to be paid = $8120 Answer
Similar Questions
(1) What amount does William have to pay after 5 years if he takes a loan of $3500 at 8% simple interest?
(2) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 3 years.
(3) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(4) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 3 years.
(6) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.
(7) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 8 years.
(9) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 8 years.
(10) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?