Question:
Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 8 years.
Correct Answer
$7350
Solution And Explanation
Solution
Given,
Principal (P) = $5250
Rate of Simple Interest (SI) = 5%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 8
= $5250 ×5/100 × 8
= 5250 × 5 × 8/100
= 26250 × 8/100
= 210000/100
= $2100
Thus, Simple Interest = $2100
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 + $2100
= $7350
Thus, Amount to be paid = $7350 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) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5250 + ($5250 × 5% × 8)
= $5250 + ($5250 ×5/100 × 8)
= $5250 + (5250 × 5 × 8/100)
= $5250 + (26250 × 8/100)
= $5250 + (210000/100)
= $5250 + $2100 = $7350
Thus, Amount (A) to be paid = $7350 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5250, the simple interest in 1 year
= 5/100 × 5250
= 5 × 5250/100
= 26250/100 = $262.5
Thus, simple interest for 1 year = $262.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $262.5 × 8 = $2100
Thus, Simple Interest (SI) = $2100
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5250 + $2100
= $7350
Thus, Amount to be paid = $7350 Answer
Similar Questions
(1) Sarah had to pay $4427.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 9% simple interest?
(3) How much loan did Amanda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8580 to clear it?
(4) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 4 years.
(6) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 3 years.
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 7 years.
(9) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.
(10) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.