Question:
Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.
Correct Answer
$7425
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 5%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 7
= $5500 ×5/100 × 7
= 5500 × 5 × 7/100
= 27500 × 7/100
= 192500/100
= $1925
Thus, Simple Interest = $1925
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 + $1925
= $7425
Thus, Amount to be paid = $7425 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) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $5500 + ($5500 × 5% × 7)
= $5500 + ($5500 ×5/100 × 7)
= $5500 + (5500 × 5 × 7/100)
= $5500 + (27500 × 7/100)
= $5500 + (192500/100)
= $5500 + $1925 = $7425
Thus, Amount (A) to be paid = $7425 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5500, the simple interest in 1 year
= 5/100 × 5500
= 5 × 5500/100
= 27500/100 = $275
Thus, simple interest for 1 year = $275
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $275 × 7 = $1925
Thus, Simple Interest (SI) = $1925
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $1925
= $7425
Thus, Amount to be paid = $7425 Answer
Similar Questions
(1) If Charles borrowed $3900 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(2) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.
(4) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(5) In how much time a principal of $3100 will amount to $3348 at a simple interest of 2% per annum?
(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 3 years.
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 8 years.
(8) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.
(10) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 9% simple interest?