Question:
Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 8 years.
Correct Answer
$9460
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 9%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 8
= $5500 ×9/100 × 8
= 5500 × 9 × 8/100
= 49500 × 8/100
= 396000/100
= $3960
Thus, Simple Interest = $3960
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 + $3960
= $9460
Thus, Amount to be paid = $9460 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) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5500 + ($5500 × 9% × 8)
= $5500 + ($5500 ×9/100 × 8)
= $5500 + (5500 × 9 × 8/100)
= $5500 + (49500 × 8/100)
= $5500 + (396000/100)
= $5500 + $3960 = $9460
Thus, Amount (A) to be paid = $9460 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5500, the simple interest in 1 year
= 9/100 × 5500
= 9 × 5500/100
= 49500/100 = $495
Thus, simple interest for 1 year = $495
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $495 × 8 = $3960
Thus, Simple Interest (SI) = $3960
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $3960
= $9460
Thus, Amount to be paid = $9460 Answer
Similar Questions
(1) What amount does David have to pay after 6 years if he takes a loan of $3400 at 4% simple interest?
(2) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.
(4) 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.
(5) Michael had to pay $3597 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) If Elizabeth borrowed $3450 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.
(8) If Margaret paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 4 years.
(10) Joshua had to pay $5194 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.