Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 8 years.
Correct Answer
$8436
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 6%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 8
= $5700 ×6/100 × 8
= 5700 × 6 × 8/100
= 34200 × 8/100
= 273600/100
= $2736
Thus, Simple Interest = $2736
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 + $2736
= $8436
Thus, Amount to be paid = $8436 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) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5700 + ($5700 × 6% × 8)
= $5700 + ($5700 ×6/100 × 8)
= $5700 + (5700 × 6 × 8/100)
= $5700 + (34200 × 8/100)
= $5700 + (273600/100)
= $5700 + $2736 = $8436
Thus, Amount (A) to be paid = $8436 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5700, the simple interest in 1 year
= 6/100 × 5700
= 6 × 5700/100
= 34200/100 = $342
Thus, simple interest for 1 year = $342
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $342 × 8 = $2736
Thus, Simple Interest (SI) = $2736
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $2736
= $8436
Thus, Amount to be paid = $8436 Answer
Similar Questions
(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 4 years.
(2) What amount does James have to pay after 6 years if he takes a loan of $3000 at 4% simple interest?
(3) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.
(4) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(5) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8580 to clear it?
(6) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.
(7) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?
(8) Richard had to pay $3924 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?
(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 7 years.