Question:
Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 8 years.
Correct Answer
$8856
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 8%
Time (t) = 8 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% × 8
= $5400 ×8/100 × 8
= 5400 × 8 × 8/100
= 43200 × 8/100
= 345600/100
= $3456
Thus, Simple Interest = $3456
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 + $3456
= $8856
Thus, Amount to be paid = $8856 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) = 8 years
Thus, Amount (A)
= $5400 + ($5400 × 8% × 8)
= $5400 + ($5400 ×8/100 × 8)
= $5400 + (5400 × 8 × 8/100)
= $5400 + (43200 × 8/100)
= $5400 + (345600/100)
= $5400 + $3456 = $8856
Thus, Amount (A) to be paid = $8856 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 8 years
= Simple interest for 1 year × 8
= $432 × 8 = $3456
Thus, Simple Interest (SI) = $3456
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $3456
= $8856
Thus, Amount to be paid = $8856 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.
(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.
(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 7 years.
(4) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 8 years.
(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 4 years.
(7) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(8) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?
(9) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.
(10) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?