Question:
Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 8 years.
Correct Answer
$8424
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 7%
Time (t) = 8 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% × 8
= $5400 ×7/100 × 8
= 5400 × 7 × 8/100
= 37800 × 8/100
= 302400/100
= $3024
Thus, Simple Interest = $3024
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 + $3024
= $8424
Thus, Amount to be paid = $8424 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) = 8 years
Thus, Amount (A)
= $5400 + ($5400 × 7% × 8)
= $5400 + ($5400 ×7/100 × 8)
= $5400 + (5400 × 7 × 8/100)
= $5400 + (37800 × 8/100)
= $5400 + (302400/100)
= $5400 + $3024 = $8424
Thus, Amount (A) to be paid = $8424 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 8 years
= Simple interest for 1 year × 8
= $378 × 8 = $3024
Thus, Simple Interest (SI) = $3024
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $3024
= $8424
Thus, Amount to be paid = $8424 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 4 years.
(3) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?
(4) How much loan did Emily borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7762.5 to clear it?
(5) How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?
(6) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.
(7) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?
(8) If Sandra paid $5340 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(10) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 2% simple interest?