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) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 3 years.
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.
(3) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 3 years.
(5) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 3 years.
(6) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 5% per annum?
(7) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10824 to clear the loan, then find the time period of the loan.
(8) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.
(10) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 5% simple interest.