Question:
Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
Correct Answer
$9595
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 10%
Time (t) = 9 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% × 9
= $5050 ×10/100 × 9
= 5050 × 10 × 9/100
= 50500 × 9/100
= 454500/100
= $4545
Thus, Simple Interest = $4545
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 + $4545
= $9595
Thus, Amount to be paid = $9595 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) = 9 years
Thus, Amount (A)
= $5050 + ($5050 × 10% × 9)
= $5050 + ($5050 ×10/100 × 9)
= $5050 + (5050 × 10 × 9/100)
= $5050 + (50500 × 9/100)
= $5050 + (454500/100)
= $5050 + $4545 = $9595
Thus, Amount (A) to be paid = $9595 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 9 years
= Simple interest for 1 year × 9
= $505 × 9 = $4545
Thus, Simple Interest (SI) = $4545
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $4545
= $9595
Thus, Amount to be paid = $9595 Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 4 years.
(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 4 years.
(4) In how much time a principal of $3000 will amount to $3270 at a simple interest of 3% per annum?
(5) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8046 to clear the loan, then find the time period of the loan.
(6) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.
(8) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 7 years.
(10) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?