Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 8 years.
Correct Answer
$8686
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 9%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 8
= $5050 ×9/100 × 8
= 5050 × 9 × 8/100
= 45450 × 8/100
= 363600/100
= $3636
Thus, Simple Interest = $3636
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 + $3636
= $8686
Thus, Amount to be paid = $8686 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) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5050 + ($5050 × 9% × 8)
= $5050 + ($5050 ×9/100 × 8)
= $5050 + (5050 × 9 × 8/100)
= $5050 + (45450 × 8/100)
= $5050 + (363600/100)
= $5050 + $3636 = $8686
Thus, Amount (A) to be paid = $8686 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5050, the simple interest in 1 year
= 9/100 × 5050
= 9 × 5050/100
= 45450/100 = $454.5
Thus, simple interest for 1 year = $454.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $454.5 × 8 = $3636
Thus, Simple Interest (SI) = $3636
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $3636
= $8686
Thus, Amount to be paid = $8686 Answer
Similar Questions
(1) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 4% simple interest?
(2) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?
(4) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.
(5) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?
(6) If Jessica borrowed $3750 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 4 years.
(8) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.