Question:
Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
Correct Answer
$6985
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 3%
Time (t) = 9 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% × 9
= $5500 ×3/100 × 9
= 5500 × 3 × 9/100
= 16500 × 9/100
= 148500/100
= $1485
Thus, Simple Interest = $1485
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 + $1485
= $6985
Thus, Amount to be paid = $6985 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) = 9 years
Thus, Amount (A)
= $5500 + ($5500 × 3% × 9)
= $5500 + ($5500 ×3/100 × 9)
= $5500 + (5500 × 3 × 9/100)
= $5500 + (16500 × 9/100)
= $5500 + (148500/100)
= $5500 + $1485 = $6985
Thus, Amount (A) to be paid = $6985 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 9 years
= Simple interest for 1 year × 9
= $165 × 9 = $1485
Thus, Simple Interest (SI) = $1485
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $1485
= $6985
Thus, Amount to be paid = $6985 Answer
Similar Questions
(1) If Kenneth paid $5800 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 3 years.
(4) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 4 years.
(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 8 years.
(7) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?
(8) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?
(10) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.