Question:
Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
Correct Answer
$8470
Solution And Explanation
Solution
Given,
Principal (P) = $5500
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) = $5500 × 6% × 9
= $5500 ×6/100 × 9
= 5500 × 6 × 9/100
= 33000 × 9/100
= 297000/100
= $2970
Thus, Simple Interest = $2970
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 + $2970
= $8470
Thus, Amount to be paid = $8470 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) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5500 + ($5500 × 6% × 9)
= $5500 + ($5500 ×6/100 × 9)
= $5500 + (5500 × 6 × 9/100)
= $5500 + (33000 × 9/100)
= $5500 + (297000/100)
= $5500 + $2970 = $8470
Thus, Amount (A) to be paid = $8470 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 $5500, the simple interest in 1 year
= 6/100 × 5500
= 6 × 5500/100
= 33000/100 = $330
Thus, simple interest for 1 year = $330
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $330 × 9 = $2970
Thus, Simple Interest (SI) = $2970
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $2970
= $8470
Thus, Amount to be paid = $8470 Answer
Similar Questions
(1) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(2) What amount does James have to pay after 6 years if he takes a loan of $3000 at 6% simple interest?
(3) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 6% simple interest.
(4) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9348 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.
(6) How much loan did James borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5500 to clear it?
(7) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 7% simple interest?
(8) Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) If Emily paid $5130 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 8 years.