Question:
Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
Correct Answer
$5959
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 2%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 9
= $5050 ×2/100 × 9
= 5050 × 2 × 9/100
= 10100 × 9/100
= 90900/100
= $909
Thus, Simple Interest = $909
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 + $909
= $5959
Thus, Amount to be paid = $5959 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) = 2%
And, Time (t) = 9 years
Thus, Amount (A)
= $5050 + ($5050 × 2% × 9)
= $5050 + ($5050 ×2/100 × 9)
= $5050 + (5050 × 2 × 9/100)
= $5050 + (10100 × 9/100)
= $5050 + (90900/100)
= $5050 + $909 = $5959
Thus, Amount (A) to be paid = $5959 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5050, the simple interest in 1 year
= 2/100 × 5050
= 2 × 5050/100
= 10100/100 = $101
Thus, simple interest for 1 year = $101
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $101 × 9 = $909
Thus, Simple Interest (SI) = $909
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $909
= $5959
Thus, Amount to be paid = $5959 Answer
Similar Questions
(1) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 3 years.
(2) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.
(3) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.
(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 7 years.
(5) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?
(6) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
(7) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?
(8) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 10% simple interest?
(9) If Barbara paid $4118 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.