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) How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?
(2) Susan had to pay $3869 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 8 years.
(4) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(5) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3200 will amount to $3520 at a simple interest of 2% per annum?
(7) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.
(8) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(9) 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.
(10) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.