Question:
Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 8 years.
Correct Answer
$6696
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 8
= $5400 ×3/100 × 8
= 5400 × 3 × 8/100
= 16200 × 8/100
= 129600/100
= $1296
Thus, Simple Interest = $1296
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 + $1296
= $6696
Thus, Amount to be paid = $6696 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5400 + ($5400 × 3% × 8)
= $5400 + ($5400 ×3/100 × 8)
= $5400 + (5400 × 3 × 8/100)
= $5400 + (16200 × 8/100)
= $5400 + (129600/100)
= $5400 + $1296 = $6696
Thus, Amount (A) to be paid = $6696 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5400, the simple interest in 1 year
= 3/100 × 5400
= 3 × 5400/100
= 16200/100 = $162
Thus, simple interest for 1 year = $162
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $162 × 8 = $1296
Thus, Simple Interest (SI) = $1296
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $1296
= $6696
Thus, Amount to be paid = $6696 Answer
Similar Questions
(1) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 4 years.
(2) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 6% simple interest?
(4) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(5) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(6) Kimberly had to pay $5068.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.
(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 7% simple interest?
(9) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.
(10) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.