Question:
Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.
Correct Answer
$7322.5
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 5%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 9
= $5050 ×5/100 × 9
= 5050 × 5 × 9/100
= 25250 × 9/100
= 227250/100
= $2272.5
Thus, Simple Interest = $2272.5
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 + $2272.5
= $7322.5
Thus, Amount to be paid = $7322.5 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) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5050 + ($5050 × 5% × 9)
= $5050 + ($5050 ×5/100 × 9)
= $5050 + (5050 × 5 × 9/100)
= $5050 + (25250 × 9/100)
= $5050 + (227250/100)
= $5050 + $2272.5 = $7322.5
Thus, Amount (A) to be paid = $7322.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5050, the simple interest in 1 year
= 5/100 × 5050
= 5 × 5050/100
= 25250/100 = $252.5
Thus, simple interest for 1 year = $252.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $252.5 × 9 = $2272.5
Thus, Simple Interest (SI) = $2272.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $2272.5
= $7322.5
Thus, Amount to be paid = $7322.5 Answer
Similar Questions
(1) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 7% simple interest?
(2) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.
(4) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.
(5) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.
(6) 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.
(7) If Susan paid $4234 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.
(9) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.
(10) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.