Question:
Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 8 years.
Correct Answer
$9720
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 10%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $5400 × 10% × 8
= $5400 ×10/100 × 8
= 5400 × 10 × 8/100
= 54000 × 8/100
= 432000/100
= $4320
Thus, Simple Interest = $4320
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 = $5400 + $4320
= $9720
Thus, Amount to be paid = $9720 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 = $5400
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5400 + ($5400 × 10% × 8)
= $5400 + ($5400 ×10/100 × 8)
= $5400 + (5400 × 10 × 8/100)
= $5400 + (54000 × 8/100)
= $5400 + (432000/100)
= $5400 + $4320 = $9720
Thus, Amount (A) to be paid = $9720 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5400, the simple interest in 1 year
= 10/100 × 5400
= 10 × 5400/100
= 54000/100 = $540
Thus, simple interest for 1 year = $540
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $540 × 8 = $4320
Thus, Simple Interest (SI) = $4320
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $4320
= $9720
Thus, Amount to be paid = $9720 Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6120 to clear the loan, then find the time period of the loan.
(2) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 3 years.
(4) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.
(5) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.
(6) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 9% simple interest?
(7) Betty had to pay $4505 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 7% simple interest?
(9) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(10) If Nancy paid $4482 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.