Question:
Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 7% simple interest.
Correct Answer
$9180
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 7%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 10
= $5400 ×7/100 × 10
= 5400 × 7 × 10/100
= 37800 × 10/100
= 378000/100
= $3780
Thus, Simple Interest = $3780
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 + $3780
= $9180
Thus, Amount to be paid = $9180 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) = 7%
And, Time (t) = 10 years
Thus, Amount (A)
= $5400 + ($5400 × 7% × 10)
= $5400 + ($5400 ×7/100 × 10)
= $5400 + (5400 × 7 × 10/100)
= $5400 + (37800 × 10/100)
= $5400 + (378000/100)
= $5400 + $3780 = $9180
Thus, Amount (A) to be paid = $9180 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5400, the simple interest in 1 year
= 7/100 × 5400
= 7 × 5400/100
= 37800/100 = $378
Thus, simple interest for 1 year = $378
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $378 × 10 = $3780
Thus, Simple Interest (SI) = $3780
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $3780
= $9180
Thus, Amount to be paid = $9180 Answer
Similar Questions
(1) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 8% simple interest?
(2) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?
(3) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.
(4) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(5) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.
(6) Michael had to pay $3795 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?
(8) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 8% simple interest?
(9) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
(10) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.