Question:
Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.
Correct Answer
$9975
Solution And Explanation
Solution
Given,
Principal (P) = $5250
Rate of Simple Interest (SI) = 9%
Time (t) = 10 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) = $5250 × 9% × 10
= $5250 ×9/100 × 10
= 5250 × 9 × 10/100
= 47250 × 10/100
= 472500/100
= $4725
Thus, Simple Interest = $4725
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 = $5250 + $4725
= $9975
Thus, Amount to be paid = $9975 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 = $5250
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5250 + ($5250 × 9% × 10)
= $5250 + ($5250 ×9/100 × 10)
= $5250 + (5250 × 9 × 10/100)
= $5250 + (47250 × 10/100)
= $5250 + (472500/100)
= $5250 + $4725 = $9975
Thus, Amount (A) to be paid = $9975 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 $5250, the simple interest in 1 year
= 9/100 × 5250
= 9 × 5250/100
= 47250/100 = $472.5
Thus, simple interest for 1 year = $472.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $472.5 × 10 = $4725
Thus, Simple Interest (SI) = $4725
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5250 + $4725
= $9975
Thus, Amount to be paid = $9975 Answer
Similar Questions
(1) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 4 years.
(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 3 years.
(3) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5576 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Susan borrowed a sum of $3650 at 8% simple interest for 4 years.
(5) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 4 years.
(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 8 years.
(8) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?
(9) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 3 years.