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) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 6% simple interest?
(2) How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?
(3) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?
(4) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 4 years.
(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 4 years.
(6) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?
(7) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(8) Joshua had to pay $5341 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.
(10) Matthew had to pay $4704 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.