Question:
Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 8 years.
Correct Answer
$7992
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 6%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 8
= $5400 ×6/100 × 8
= 5400 × 6 × 8/100
= 32400 × 8/100
= 259200/100
= $2592
Thus, Simple Interest = $2592
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 + $2592
= $7992
Thus, Amount to be paid = $7992 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) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5400 + ($5400 × 6% × 8)
= $5400 + ($5400 ×6/100 × 8)
= $5400 + (5400 × 6 × 8/100)
= $5400 + (32400 × 8/100)
= $5400 + (259200/100)
= $5400 + $2592 = $7992
Thus, Amount (A) to be paid = $7992 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5400, the simple interest in 1 year
= 6/100 × 5400
= 6 × 5400/100
= 32400/100 = $324
Thus, simple interest for 1 year = $324
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $324 × 8 = $2592
Thus, Simple Interest (SI) = $2592
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $2592
= $7992
Thus, Amount to be paid = $7992 Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
(3) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 7 years.
(5) How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?
(6) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.
(7) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.
(8) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(9) Matthew had to pay $4830 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 3% simple interest.