Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 8 years.
Correct Answer
$8892
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 7%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 8
= $5700 ×7/100 × 8
= 5700 × 7 × 8/100
= 39900 × 8/100
= 319200/100
= $3192
Thus, Simple Interest = $3192
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 + $3192
= $8892
Thus, Amount to be paid = $8892 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) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5700 + ($5700 × 7% × 8)
= $5700 + ($5700 ×7/100 × 8)
= $5700 + (5700 × 7 × 8/100)
= $5700 + (39900 × 8/100)
= $5700 + (319200/100)
= $5700 + $3192 = $8892
Thus, Amount (A) to be paid = $8892 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5700, the simple interest in 1 year
= 7/100 × 5700
= 7 × 5700/100
= 39900/100 = $399
Thus, simple interest for 1 year = $399
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $399 × 8 = $3192
Thus, Simple Interest (SI) = $3192
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $3192
= $8892
Thus, Amount to be paid = $8892 Answer
Similar Questions
(1) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9437.5 to clear it?
(2) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 8 years.
(4) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 8% simple interest?
(5) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 3 years.
(6) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?
(7) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.
(8) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 7 years.
(10) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.