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) If Charles paid $4524 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) What amount will be due after 2 years if William borrowed a sum of $3250 at a 7% simple interest?
(3) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?
(4) If Richard borrowed $3600 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 3 years.
(6) How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?
(7) How much loan did Amanda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8580 to clear it?
(8) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 7 years.
(10) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?