Question:
Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 8 years.
Correct Answer
$9288
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 9%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 8
= $5400 ×9/100 × 8
= 5400 × 9 × 8/100
= 48600 × 8/100
= 388800/100
= $3888
Thus, Simple Interest = $3888
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 + $3888
= $9288
Thus, Amount to be paid = $9288 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) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5400 + ($5400 × 9% × 8)
= $5400 + ($5400 ×9/100 × 8)
= $5400 + (5400 × 9 × 8/100)
= $5400 + (48600 × 8/100)
= $5400 + (388800/100)
= $5400 + $3888 = $9288
Thus, Amount (A) to be paid = $9288 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5400, the simple interest in 1 year
= 9/100 × 5400
= 9 × 5400/100
= 48600/100 = $486
Thus, simple interest for 1 year = $486
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $486 × 8 = $3888
Thus, Simple Interest (SI) = $3888
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $3888
= $9288
Thus, Amount to be paid = $9288 Answer
Similar Questions
(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 7 years.
(2) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 6% simple interest?
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 4 years.
(4) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.
(5) If Charles paid $4680 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 4 years.
(7) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if James borrowed a sum of $3000 at a 7% simple interest?
(9) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 7 years.