Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 8 years.
Correct Answer
$10530
Solution And Explanation
Solution
Given,
Principal (P) = $5850
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) = $5850 × 10% × 8
= $5850 ×10/100 × 8
= 5850 × 10 × 8/100
= 58500 × 8/100
= 468000/100
= $4680
Thus, Simple Interest = $4680
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 = $5850 + $4680
= $10530
Thus, Amount to be paid = $10530 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 = $5850
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5850 + ($5850 × 10% × 8)
= $5850 + ($5850 ×10/100 × 8)
= $5850 + (5850 × 10 × 8/100)
= $5850 + (58500 × 8/100)
= $5850 + (468000/100)
= $5850 + $4680 = $10530
Thus, Amount (A) to be paid = $10530 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 $5850, the simple interest in 1 year
= 10/100 × 5850
= 10 × 5850/100
= 58500/100 = $585
Thus, simple interest for 1 year = $585
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $585 × 8 = $4680
Thus, Simple Interest (SI) = $4680
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $4680
= $10530
Thus, Amount to be paid = $10530 Answer
Similar Questions
(1) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 3% simple interest.
(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.
(3) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.
(4) In how much time a principal of $3100 will amount to $3875 at a simple interest of 5% per annum?
(5) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(6) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.
(7) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7748 to clear the loan, then find the time period of the loan.
(8) 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.
(9) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 6% simple interest.
(10) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?