Question:
Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
Correct Answer
$10100
Solution And Explanation
Solution
Given,
Principal (P) = $5050
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) = $5050 × 10% × 10
= $5050 ×10/100 × 10
= 5050 × 10 × 10/100
= 50500 × 10/100
= 505000/100
= $5050
Thus, Simple Interest = $5050
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 + $5050
= $10100
Thus, Amount to be paid = $10100 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) = 10%
And, Time (t) = 10 years
Thus, Amount (A)
= $5050 + ($5050 × 10% × 10)
= $5050 + ($5050 ×10/100 × 10)
= $5050 + (5050 × 10 × 10/100)
= $5050 + (50500 × 10/100)
= $5050 + (505000/100)
= $5050 + $5050 = $10100
Thus, Amount (A) to be paid = $10100 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 $5050, the simple interest in 1 year
= 10/100 × 5050
= 10 × 5050/100
= 50500/100 = $505
Thus, simple interest for 1 year = $505
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $505 × 10 = $5050
Thus, Simple Interest (SI) = $5050
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $5050
= $10100
Thus, Amount to be paid = $10100 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
(2) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.
(3) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?
(4) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 8% simple interest?
(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 3 years.
(6) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?
(7) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
(8) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 4 years.
(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 2% simple interest.
(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 4 years.