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) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.
(2) Donna had to pay $5432 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 7% simple interest?
(4) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 4 years.
(5) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.
(7) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(9) If David paid $3944 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) How much loan did Sandra borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8062.5 to clear it?