Question:
Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 7 years.
Correct Answer
$8925
Solution And Explanation
Solution
Given,
Principal (P) = $5250
Rate of Simple Interest (SI) = 10%
Time (t) = 7 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% × 7
= $5250 ×10/100 × 7
= 5250 × 10 × 7/100
= 52500 × 7/100
= 367500/100
= $3675
Thus, Simple Interest = $3675
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 + $3675
= $8925
Thus, Amount to be paid = $8925 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) = 7 years
Thus, Amount (A)
= $5250 + ($5250 × 10% × 7)
= $5250 + ($5250 ×10/100 × 7)
= $5250 + (5250 × 10 × 7/100)
= $5250 + (52500 × 7/100)
= $5250 + (367500/100)
= $5250 + $3675 = $8925
Thus, Amount (A) to be paid = $8925 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 7 years
= Simple interest for 1 year × 7
= $525 × 7 = $3675
Thus, Simple Interest (SI) = $3675
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5250 + $3675
= $8925
Thus, Amount to be paid = $8925 Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.
(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 3 years.
(4) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7748 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 4 years.
(6) If Betty paid $4590 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 7 years.
(8) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(9) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(10) Sarah had to pay $4196.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.