Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.
Correct Answer
$6786
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 2%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 8
= $5850 ×2/100 × 8
= 5850 × 2 × 8/100
= 11700 × 8/100
= 93600/100
= $936
Thus, Simple Interest = $936
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 + $936
= $6786
Thus, Amount to be paid = $6786 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) = 2%
And, Time (t) = 8 years
Thus, Amount (A)
= $5850 + ($5850 × 2% × 8)
= $5850 + ($5850 ×2/100 × 8)
= $5850 + (5850 × 2 × 8/100)
= $5850 + (11700 × 8/100)
= $5850 + (93600/100)
= $5850 + $936 = $6786
Thus, Amount (A) to be paid = $6786 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5850, the simple interest in 1 year
= 2/100 × 5850
= 2 × 5850/100
= 11700/100 = $117
Thus, simple interest for 1 year = $117
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $117 × 8 = $936
Thus, Simple Interest (SI) = $936
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $936
= $6786
Thus, Amount to be paid = $6786 Answer
Similar Questions
(1) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.
(3) How much loan did Mary borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6060 to clear it?
(4) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9112 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 9% simple interest.
(6) In how much time a principal of $3100 will amount to $3348 at a simple interest of 4% per annum?
(7) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.
(8) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 6% simple interest?
(9) If Lisa paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.