Question:
Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
Correct Answer
$9546
Solution And Explanation
Solution
Given,
Principal (P) = $5550
Rate of Simple Interest (SI) = 8%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $5550 × 8% × 9
= $5550 ×8/100 × 9
= 5550 × 8 × 9/100
= 44400 × 9/100
= 399600/100
= $3996
Thus, Simple Interest = $3996
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 = $5550 + $3996
= $9546
Thus, Amount to be paid = $9546 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 = $5550
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5550 + ($5550 × 8% × 9)
= $5550 + ($5550 ×8/100 × 9)
= $5550 + (5550 × 8 × 9/100)
= $5550 + (44400 × 9/100)
= $5550 + (399600/100)
= $5550 + $3996 = $9546
Thus, Amount (A) to be paid = $9546 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5550, the simple interest in 1 year
= 8/100 × 5550
= 8 × 5550/100
= 44400/100 = $444
Thus, simple interest for 1 year = $444
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $444 × 9 = $3996
Thus, Simple Interest (SI) = $3996
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $3996
= $9546
Thus, Amount to be paid = $9546 Answer
Similar Questions
(1) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 9% simple interest?
(2) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 10% simple interest?
(3) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 7 years.
(4) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.
(5) 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.
(6) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(7) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 8 years.
(9) How much loan did Donald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7150 to clear it?
(10) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.