Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.
Correct Answer
$5858
Solution And Explanation
Solution
Given,
Principal (P) = $5050
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) = $5050 × 2% × 8
= $5050 ×2/100 × 8
= 5050 × 2 × 8/100
= 10100 × 8/100
= 80800/100
= $808
Thus, Simple Interest = $808
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 = $5050 + $808
= $5858
Thus, Amount to be paid = $5858 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 = $5050
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 8 years
Thus, Amount (A)
= $5050 + ($5050 × 2% × 8)
= $5050 + ($5050 ×2/100 × 8)
= $5050 + (5050 × 2 × 8/100)
= $5050 + (10100 × 8/100)
= $5050 + (80800/100)
= $5050 + $808 = $5858
Thus, Amount (A) to be paid = $5858 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 $5050, the simple interest in 1 year
= 2/100 × 5050
= 2 × 5050/100
= 10100/100 = $101
Thus, simple interest for 1 year = $101
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $101 × 8 = $808
Thus, Simple Interest (SI) = $808
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $808
= $5858
Thus, Amount to be paid = $5858 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(2) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.
(3) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7599 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 3 years.
(5) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.
(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 8 years.
(7) If Emily paid $5510 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 9% simple interest?
(9) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $14000 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 3 years.