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) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.
(2) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
(4) Susan had to pay $3869 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7700 to clear it?
(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 3 years.
(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 8 years.
(8) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.
(9) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.
(10) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.