Question:
Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
Correct Answer
$8085
Solution And Explanation
Solution
Given,
Principal (P) = $5250
Rate of Simple Interest (SI) = 6%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 9
= $5250 ×6/100 × 9
= 5250 × 6 × 9/100
= 31500 × 9/100
= 283500/100
= $2835
Thus, Simple Interest = $2835
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 + $2835
= $8085
Thus, Amount to be paid = $8085 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) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5250 + ($5250 × 6% × 9)
= $5250 + ($5250 ×6/100 × 9)
= $5250 + (5250 × 6 × 9/100)
= $5250 + (31500 × 9/100)
= $5250 + (283500/100)
= $5250 + $2835 = $8085
Thus, Amount (A) to be paid = $8085 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5250, the simple interest in 1 year
= 6/100 × 5250
= 6 × 5250/100
= 31500/100 = $315
Thus, simple interest for 1 year = $315
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $315 × 9 = $2835
Thus, Simple Interest (SI) = $2835
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5250 + $2835
= $8085
Thus, Amount to be paid = $8085 Answer
Similar Questions
(1) Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) How much loan did Laura borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9027.5 to clear it?
(3) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
(4) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(5) Daniel had to pay $4346 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) In how much time a principal of $3000 will amount to $3270 at a simple interest of 3% per annum?
(8) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Susan borrowed a sum of $3650 at 3% simple interest for 3 years.
(10) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?