Question:
Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
Correct Answer
$9500
Solution And Explanation
Solution
Given,
Principal (P) = $5000
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) = $5000 × 10% × 9
= $5000 ×10/100 × 9
= 5000 × 10 × 9/100
= 50000 × 9/100
= 450000/100
= $4500
Thus, Simple Interest = $4500
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 = $5000 + $4500
= $9500
Thus, Amount to be paid = $9500 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 = $5000
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5000 + ($5000 × 10% × 9)
= $5000 + ($5000 ×10/100 × 9)
= $5000 + (5000 × 10 × 9/100)
= $5000 + (50000 × 9/100)
= $5000 + (450000/100)
= $5000 + $4500 = $9500
Thus, Amount (A) to be paid = $9500 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 $5000, the simple interest in 1 year
= 10/100 × 5000
= 10 × 5000/100
= 50000/100 = $500
Thus, simple interest for 1 year = $500
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $500 × 9 = $4500
Thus, Simple Interest (SI) = $4500
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $4500
= $9500
Thus, Amount to be paid = $9500 Answer
Similar Questions
(1) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.
(2) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 8% simple interest?
(3) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
(4) How much loan did Steven borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7260 to clear it?
(5) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 7 years.
(6) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 8% simple interest?
(9) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 3% simple interest?
(10) How much loan did Lisa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6957.5 to clear it?