Question:
Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
Correct Answer
$7700
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 4%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 10
= $5500 ×4/100 × 10
= 5500 × 4 × 10/100
= 22000 × 10/100
= 220000/100
= $2200
Thus, Simple Interest = $2200
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 + $2200
= $7700
Thus, Amount to be paid = $7700 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) = 4%
And, Time (t) = 10 years
Thus, Amount (A)
= $5500 + ($5500 × 4% × 10)
= $5500 + ($5500 ×4/100 × 10)
= $5500 + (5500 × 4 × 10/100)
= $5500 + (22000 × 10/100)
= $5500 + (220000/100)
= $5500 + $2200 = $7700
Thus, Amount (A) to be paid = $7700 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5500, the simple interest in 1 year
= 4/100 × 5500
= 4 × 5500/100
= 22000/100 = $220
Thus, simple interest for 1 year = $220
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $220 × 10 = $2200
Thus, Simple Interest (SI) = $2200
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $2200
= $7700
Thus, Amount to be paid = $7700 Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?
(3) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.
(4) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
(5) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 3 years.
(6) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.
(8) Joshua had to pay $5635 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) If Paul paid $5264 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 2% simple interest?