Question : Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
Correct Answer $10000
Solution & Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 10%
Time (t) = 10 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) = $5000 × 10% × 10
= $5000 ×10/100 × 10
= 5000 × 10 × 10/100
= 50000 × 10/100
= 500000/100
= $5000
Thus, Simple Interest = $5000
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 + $5000
= $10000
Thus, Amount to be paid = $10000 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) = 10%
And, Time (t) = 10 years
Thus, Amount (A)
= $5000 + ($5000 × 10% × 10)
= $5000 + ($5000 ×10/100 × 10)
= $5000 + (5000 × 10 × 10/100)
= $5000 + (50000 × 10/100)
= $5000 + (500000/100)
= $5000 + $5000 = $10000
Thus, Amount (A) to be paid = $10000 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 $5000, the simple interest in 1 year
= 10/100 × 5000
= 10 × 5000/100
= 50000/100 = $500
Thus, simple interest for 1 year = $500
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $500 × 10 = $5000
Thus, Simple Interest (SI) = $5000
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $5000
= $10000
Thus, Amount to be paid = $10000 Answer
Similar Questions
(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 8 years.
(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 8 years.
(3) What amount does James have to pay after 6 years if he takes a loan of $3000 at 8% simple interest?
(5) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 3 years.
(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 8 years.
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 4 years.