Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.
Correct Answer
$7524
Solution And Explanation
Solution
Given,
Principal (P) = $5700
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) = $5700 × 4% × 8
= $5700 ×4/100 × 8
= 5700 × 4 × 8/100
= 22800 × 8/100
= 182400/100
= $1824
Thus, Simple Interest = $1824
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 = $5700 + $1824
= $7524
Thus, Amount to be paid = $7524 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 = $5700
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5700 + ($5700 × 4% × 8)
= $5700 + ($5700 ×4/100 × 8)
= $5700 + (5700 × 4 × 8/100)
= $5700 + (22800 × 8/100)
= $5700 + (182400/100)
= $5700 + $1824 = $7524
Thus, Amount (A) to be paid = $7524 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 $5700, the simple interest in 1 year
= 4/100 × 5700
= 4 × 5700/100
= 22800/100 = $228
Thus, simple interest for 1 year = $228
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $228 × 8 = $1824
Thus, Simple Interest (SI) = $1824
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $1824
= $7524
Thus, Amount to be paid = $7524 Answer
Similar Questions
(1) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 8% simple interest?
(2) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 3 years.
(4) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 4 years.
(5) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7421 to clear the loan, then find the time period of the loan.
(6) If Nancy paid $4814 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.
(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 7 years.
(9) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 8 years.
(10) If Ashley paid $5278 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.