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) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 2% simple interest?
(2) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.
(3) What amount does David have to pay after 6 years if he takes a loan of $3400 at 7% simple interest?
(4) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.
(5) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(6) What amount does John have to pay after 6 years if he takes a loan of $3200 at 5% simple interest?
(7) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.
(8) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 3 years.
(10) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.