Question:
Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
Correct Answer
$8150
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 7%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 9
= $5000 ×7/100 × 9
= 5000 × 7 × 9/100
= 35000 × 9/100
= 315000/100
= $3150
Thus, Simple Interest = $3150
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 + $3150
= $8150
Thus, Amount to be paid = $8150 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) = 7%
And, Time (t) = 9 years
Thus, Amount (A)
= $5000 + ($5000 × 7% × 9)
= $5000 + ($5000 ×7/100 × 9)
= $5000 + (5000 × 7 × 9/100)
= $5000 + (35000 × 9/100)
= $5000 + (315000/100)
= $5000 + $3150 = $8150
Thus, Amount (A) to be paid = $8150 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5000, the simple interest in 1 year
= 7/100 × 5000
= 7 × 5000/100
= 35000/100 = $350
Thus, simple interest for 1 year = $350
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $350 × 9 = $3150
Thus, Simple Interest (SI) = $3150
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $3150
= $8150
Thus, Amount to be paid = $8150 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.
(2) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.
(3) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 3 years.
(5) In how much time a principal of $3150 will amount to $3937.5 at a simple interest of 5% per annum?
(6) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.
(7) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 2% simple interest?
(8) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?
(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.
(10) How much loan did Robert borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6120 to clear it?