Question:
Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 8 years.
Correct Answer
$6820
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 8
= $5500 ×3/100 × 8
= 5500 × 3 × 8/100
= 16500 × 8/100
= 132000/100
= $1320
Thus, Simple Interest = $1320
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 + $1320
= $6820
Thus, Amount to be paid = $6820 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5500 + ($5500 × 3% × 8)
= $5500 + ($5500 ×3/100 × 8)
= $5500 + (5500 × 3 × 8/100)
= $5500 + (16500 × 8/100)
= $5500 + (132000/100)
= $5500 + $1320 = $6820
Thus, Amount (A) to be paid = $6820 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5500, the simple interest in 1 year
= 3/100 × 5500
= 3 × 5500/100
= 16500/100 = $165
Thus, simple interest for 1 year = $165
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $165 × 8 = $1320
Thus, Simple Interest (SI) = $1320
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $1320
= $6820
Thus, Amount to be paid = $6820 Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.
(2) Thomas had to pay $4142 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) If Elizabeth paid $4140 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.
(5) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.
(6) Daniel had to pay $4469 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(8) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.
(9) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 3% simple interest?