Question:
Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.
Correct Answer
$7777
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 6%
Time (t) = 9 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% × 9
= $5050 ×6/100 × 9
= 5050 × 6 × 9/100
= 30300 × 9/100
= 272700/100
= $2727
Thus, Simple Interest = $2727
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 + $2727
= $7777
Thus, Amount to be paid = $7777 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) = 9 years
Thus, Amount (A)
= $5050 + ($5050 × 6% × 9)
= $5050 + ($5050 ×6/100 × 9)
= $5050 + (5050 × 6 × 9/100)
= $5050 + (30300 × 9/100)
= $5050 + (272700/100)
= $5050 + $2727 = $7777
Thus, Amount (A) to be paid = $7777 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 9 years
= Simple interest for 1 year × 9
= $303 × 9 = $2727
Thus, Simple Interest (SI) = $2727
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $2727
= $7777
Thus, Amount to be paid = $7777 Answer
Similar Questions
(1) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 7 years.
(2) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 8% simple interest.
(3) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.
(4) If Mary borrowed $3050 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(5) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.
(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.
(7) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9142.5 to clear it?
(8) What amount does John have to pay after 5 years if he takes a loan of $3200 at 8% simple interest?
(9) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 9% simple interest.
(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 4 years.