Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.
Correct Answer
$10260
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 10%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 8
= $5700 ×10/100 × 8
= 5700 × 10 × 8/100
= 57000 × 8/100
= 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) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5700 + ($5700 × 10% × 8)
= $5700 + ($5700 ×10/100 × 8)
= $5700 + (5700 × 10 × 8/100)
= $5700 + (57000 × 8/100)
= $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 = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5700, the simple interest in 1 year
= 10/100 × 5700
= 10 × 5700/100
= 57000/100 = $570
Thus, simple interest for 1 year = $570
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $570 × 8 = $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) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 7 years.
(2) If Robert paid $3596 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 8 years.
(4) Calculate the amount due if Susan borrowed a sum of $3650 at 3% simple interest for 4 years.
(5) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.
(6) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
(8) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?
(10) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.