Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 8 years.
Correct Answer
$9348
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 8%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 8
= $5700 ×8/100 × 8
= 5700 × 8 × 8/100
= 45600 × 8/100
= 364800/100
= $3648
Thus, Simple Interest = $3648
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 + $3648
= $9348
Thus, Amount to be paid = $9348 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) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5700 + ($5700 × 8% × 8)
= $5700 + ($5700 ×8/100 × 8)
= $5700 + (5700 × 8 × 8/100)
= $5700 + (45600 × 8/100)
= $5700 + (364800/100)
= $5700 + $3648 = $9348
Thus, Amount (A) to be paid = $9348 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5700, the simple interest in 1 year
= 8/100 × 5700
= 8 × 5700/100
= 45600/100 = $456
Thus, simple interest for 1 year = $456
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $456 × 8 = $3648
Thus, Simple Interest (SI) = $3648
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $3648
= $9348
Thus, Amount to be paid = $9348 Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.
(2) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(3) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 8% simple interest?
(4) Ashley had to pay $5096 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.
(6) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.
(7) How much loan did Lisa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7260 to clear it?
(8) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 7% simple interest?
(9) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 7 years.