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) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?
(2) If Patricia paid $3528 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.
(4) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?
(5) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.
(6) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(7) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(8) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(9) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.
(10) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 2% simple interest?