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) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(2) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.
(3) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $11480 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 7 years.
(5) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(6) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 3 years.
(8) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?
(10) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 5% simple interest?