Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 7 years.
Correct Answer
$7296
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 4%
Time (t) = 7 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% × 7
= $5700 ×4/100 × 7
= 5700 × 4 × 7/100
= 22800 × 7/100
= 159600/100
= $1596
Thus, Simple Interest = $1596
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 + $1596
= $7296
Thus, Amount to be paid = $7296 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) = 7 years
Thus, Amount (A)
= $5700 + ($5700 × 4% × 7)
= $5700 + ($5700 ×4/100 × 7)
= $5700 + (5700 × 4 × 7/100)
= $5700 + (22800 × 7/100)
= $5700 + (159600/100)
= $5700 + $1596 = $7296
Thus, Amount (A) to be paid = $7296 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 7 years
= Simple interest for 1 year × 7
= $228 × 7 = $1596
Thus, Simple Interest (SI) = $1596
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $1596
= $7296
Thus, Amount to be paid = $7296 Answer
Similar Questions
(1) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7748 to clear the loan, then find the time period of the loan.
(2) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.
(3) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.
(4) How much loan did Anthony borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7245 to clear it?
(5) William had to pay $3710 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 3 years.
(8) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.
(9) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 7 years.