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) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 7 years.
(3) In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?
(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 7 years.
(5) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 4 years.
(6) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.
(7) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?
(8) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.
(10) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?