Question:
Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 2% simple interest.
Correct Answer
$6600
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 2%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 10
= $5500 ×2/100 × 10
= 5500 × 2 × 10/100
= 11000 × 10/100
= 110000/100
= $1100
Thus, Simple Interest = $1100
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 + $1100
= $6600
Thus, Amount to be paid = $6600 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) = 2%
And, Time (t) = 10 years
Thus, Amount (A)
= $5500 + ($5500 × 2% × 10)
= $5500 + ($5500 ×2/100 × 10)
= $5500 + (5500 × 2 × 10/100)
= $5500 + (11000 × 10/100)
= $5500 + (110000/100)
= $5500 + $1100 = $6600
Thus, Amount (A) to be paid = $6600 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5500, the simple interest in 1 year
= 2/100 × 5500
= 2 × 5500/100
= 11000/100 = $110
Thus, simple interest for 1 year = $110
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $110 × 10 = $1100
Thus, Simple Interest (SI) = $1100
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $1100
= $6600
Thus, Amount to be paid = $6600 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.
(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 7 years.
(3) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 8 years.
(4) If Thomas borrowed $3800 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(5) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.
(7) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7975 to clear it?
(8) If Sarah paid $4158 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) If Robert paid $3720 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.