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 John have to pay after 5 years if he takes a loan of $3200 at 8% simple interest?
(2) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.
(5) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(6) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
(8) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.
(9) If Steven paid $4968 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) John had to pay $3680 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.