Question:
Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.
Correct Answer
$9975
Solution And Explanation
Solution
Given,
Principal (P) = $5250
Rate of Simple Interest (SI) = 10%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 9
= $5250 ×10/100 × 9
= 5250 × 10 × 9/100
= 52500 × 9/100
= 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) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5250 + ($5250 × 10% × 9)
= $5250 + ($5250 ×10/100 × 9)
= $5250 + (5250 × 10 × 9/100)
= $5250 + (52500 × 9/100)
= $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 = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5250, the simple interest in 1 year
= 10/100 × 5250
= 10 × 5250/100
= 52500/100 = $525
Thus, simple interest for 1 year = $525
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $525 × 9 = $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) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(2) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?
(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.
(4) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.
(6) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 7% simple interest?
(7) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.
(9) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.
(10) Daniel had to pay $4715 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.