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) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11946 to clear the loan, then find the time period of the loan.
(2) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6407 to clear the loan, then find the time period of the loan.
(3) How much loan did Donald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8125 to clear it?
(4) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 7% simple interest?
(6) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 4 years.
(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.
(8) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
(9) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.