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) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 4 years.
(2) In how much time a principal of $3200 will amount to $3520 at a simple interest of 2% per annum?
(3) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 7% simple interest?
(5) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.
(6) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
(7) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.
(9) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.
(10) What amount does James have to pay after 6 years if he takes a loan of $3000 at 3% simple interest?