Question:
Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
Correct Answer
$10450
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 10%
Time (t) = 9 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) = $5500 × 10% × 9
= $5500 ×10/100 × 9
= 5500 × 10 × 9/100
= 55000 × 9/100
= 495000/100
= $4950
Thus, Simple Interest = $4950
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 = $5500 + $4950
= $10450
Thus, Amount to be paid = $10450 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 = $5500
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5500 + ($5500 × 10% × 9)
= $5500 + ($5500 ×10/100 × 9)
= $5500 + (5500 × 10 × 9/100)
= $5500 + (55000 × 9/100)
= $5500 + (495000/100)
= $5500 + $4950 = $10450
Thus, Amount (A) to be paid = $10450 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 $5500, the simple interest in 1 year
= 10/100 × 5500
= 10 × 5500/100
= 55000/100 = $550
Thus, simple interest for 1 year = $550
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $550 × 9 = $4950
Thus, Simple Interest (SI) = $4950
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $4950
= $10450
Thus, Amount to be paid = $10450 Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(2) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.
(4) How much loan did Daniel borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7015 to clear it?
(5) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 10% simple interest?
(6) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 8 years.
(7) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 10% simple interest?
(9) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 4 years.
(10) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.