Question:
Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 8% simple interest.
Correct Answer
$9288
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 8%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 9
= $5400 ×8/100 × 9
= 5400 × 8 × 9/100
= 43200 × 9/100
= 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) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5400 + ($5400 × 8% × 9)
= $5400 + ($5400 ×8/100 × 9)
= $5400 + (5400 × 8 × 9/100)
= $5400 + (43200 × 9/100)
= $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 = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5400, the simple interest in 1 year
= 8/100 × 5400
= 8 × 5400/100
= 43200/100 = $432
Thus, simple interest for 1 year = $432
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $432 × 9 = $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) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.
(2) Donna had to pay $5577.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) In how much time a principal of $3050 will amount to $3416 at a simple interest of 3% per annum?
(4) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.
(5) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 2% simple interest?
(6) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(7) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
(8) How much loan did David borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5940 to clear it?
(9) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(10) What amount does David have to pay after 5 years if he takes a loan of $3400 at 3% simple interest?