Question:
Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 2% simple interest.
Correct Answer
$6000
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 2%
Time (t) = 10 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) = $5000 × 2% × 10
= $5000 ×2/100 × 10
= 5000 × 2 × 10/100
= 10000 × 10/100
= 100000/100
= $1000
Thus, Simple Interest = $1000
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 = $5000 + $1000
= $6000
Thus, Amount to be paid = $6000 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 = $5000
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 10 years
Thus, Amount (A)
= $5000 + ($5000 × 2% × 10)
= $5000 + ($5000 ×2/100 × 10)
= $5000 + (5000 × 2 × 10/100)
= $5000 + (10000 × 10/100)
= $5000 + (100000/100)
= $5000 + $1000 = $6000
Thus, Amount (A) to be paid = $6000 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 $5000, the simple interest in 1 year
= 2/100 × 5000
= 2 × 5000/100
= 10000/100 = $100
Thus, simple interest for 1 year = $100
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $100 × 10 = $1000
Thus, Simple Interest (SI) = $1000
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $1000
= $6000
Thus, Amount to be paid = $6000 Answer
Similar Questions
(1) Patricia had to pay $3622.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Michael had to pay $3696 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 7 years.
(5) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
(6) If Richard paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 8% simple interest?
(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.
(9) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.
(10) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 4 years.