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) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 7 years.
(4) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.
(5) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
(6) If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) If Sarah paid $4466 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 8% simple interest?
(9) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.
(10) In how much time a principal of $3150 will amount to $3780 at a simple interest of 5% per annum?