Question:
Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.
Correct Answer
$8080
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 6%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 10
= $5050 ×6/100 × 10
= 5050 × 6 × 10/100
= 30300 × 10/100
= 303000/100
= $3030
Thus, Simple Interest = $3030
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 + $3030
= $8080
Thus, Amount to be paid = $8080 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) = 6%
And, Time (t) = 10 years
Thus, Amount (A)
= $5050 + ($5050 × 6% × 10)
= $5050 + ($5050 ×6/100 × 10)
= $5050 + (5050 × 6 × 10/100)
= $5050 + (30300 × 10/100)
= $5050 + (303000/100)
= $5050 + $3030 = $8080
Thus, Amount (A) to be paid = $8080 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5050, the simple interest in 1 year
= 6/100 × 5050
= 6 × 5050/100
= 30300/100 = $303
Thus, simple interest for 1 year = $303
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $303 × 10 = $3030
Thus, Simple Interest (SI) = $3030
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $3030
= $8080
Thus, Amount to be paid = $8080 Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $12000 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3000 will amount to $3240 at a simple interest of 4% per annum?
(3) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 3 years.
(5) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 2% simple interest.
(7) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 8 years.
(9) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(10) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?