Question:
Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 8 years.
Correct Answer
$7128
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 4%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 8
= $5400 ×4/100 × 8
= 5400 × 4 × 8/100
= 21600 × 8/100
= 172800/100
= $1728
Thus, Simple Interest = $1728
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 + $1728
= $7128
Thus, Amount to be paid = $7128 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) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5400 + ($5400 × 4% × 8)
= $5400 + ($5400 ×4/100 × 8)
= $5400 + (5400 × 4 × 8/100)
= $5400 + (21600 × 8/100)
= $5400 + (172800/100)
= $5400 + $1728 = $7128
Thus, Amount (A) to be paid = $7128 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5400, the simple interest in 1 year
= 4/100 × 5400
= 4 × 5400/100
= 21600/100 = $216
Thus, simple interest for 1 year = $216
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $216 × 8 = $1728
Thus, Simple Interest (SI) = $1728
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $1728
= $7128
Thus, Amount to be paid = $7128 Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.
(2) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 10% simple interest?
(3) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 8 years.
(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 3 years.
(5) What amount will be due after 2 years if James borrowed a sum of $3000 at a 5% simple interest?
(6) What amount does David have to pay after 6 years if he takes a loan of $3400 at 7% simple interest?
(7) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
(8) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
(10) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.