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) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.
(2) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?
(3) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 3 years.
(4) How much loan did Karen borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6842.5 to clear it?
(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 7 years.
(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.
(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 8 years.
(8) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
(9) How much loan did Sharon borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8912.5 to clear it?
(10) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10824 to clear the loan, then find the time period of the loan.