Question:
Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.
Correct Answer
$10260
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 8%
Time (t) = 10 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% × 10
= $5700 ×8/100 × 10
= 5700 × 8 × 10/100
= 45600 × 10/100
= 456000/100
= $4560
Thus, Simple Interest = $4560
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 + $4560
= $10260
Thus, Amount to be paid = $10260 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) = 10 years
Thus, Amount (A)
= $5700 + ($5700 × 8% × 10)
= $5700 + ($5700 ×8/100 × 10)
= $5700 + (5700 × 8 × 10/100)
= $5700 + (45600 × 10/100)
= $5700 + (456000/100)
= $5700 + $4560 = $10260
Thus, Amount (A) to be paid = $10260 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 10 years
= Simple interest for 1 year × 10
= $456 × 10 = $4560
Thus, Simple Interest (SI) = $4560
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $4560
= $10260
Thus, Amount to be paid = $10260 Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10660 to clear the loan, then find the time period of the loan.
(2) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 7 years.
(4) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 3 years.
(5) How much loan did Thomas borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6960 to clear it?
(6) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 3 years.
(7) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10679 to clear the loan, then find the time period of the loan.
(8) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
(10) How much loan did Jason borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9240 to clear it?