Question:
Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
Correct Answer
$7150
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 3%
Time (t) = 10 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% × 10
= $5500 ×3/100 × 10
= 5500 × 3 × 10/100
= 16500 × 10/100
= 165000/100
= $1650
Thus, Simple Interest = $1650
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 + $1650
= $7150
Thus, Amount to be paid = $7150 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) = 10 years
Thus, Amount (A)
= $5500 + ($5500 × 3% × 10)
= $5500 + ($5500 ×3/100 × 10)
= $5500 + (5500 × 3 × 10/100)
= $5500 + (16500 × 10/100)
= $5500 + (165000/100)
= $5500 + $1650 = $7150
Thus, Amount (A) to be paid = $7150 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 10 years
= Simple interest for 1 year × 10
= $165 × 10 = $1650
Thus, Simple Interest (SI) = $1650
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $1650
= $7150
Thus, Amount to be paid = $7150 Answer
Similar Questions
(1) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 10% simple interest?
(2) If Susan paid $4380 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 4 years.
(4) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
(5) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 9% simple interest?
(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 8 years.
(7) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.
(8) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.
(9) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 4% simple interest?
(10) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.