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) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if John borrowed a sum of $3100 at a 6% simple interest?
(3) 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.
(4) What amount will be due after 2 years if David borrowed a sum of $3200 at a 9% simple interest?
(5) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 4 years.
(6) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(7) How much loan did James borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5750 to clear it?
(8) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 4% simple interest?
(9) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 4 years.
(10) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?