Question:
Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 7 years.
Correct Answer
$6270
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 2%
Time (t) = 7 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% × 7
= $5500 ×2/100 × 7
= 5500 × 2 × 7/100
= 11000 × 7/100
= 77000/100
= $770
Thus, Simple Interest = $770
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 + $770
= $6270
Thus, Amount to be paid = $6270 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) = 7 years
Thus, Amount (A)
= $5500 + ($5500 × 2% × 7)
= $5500 + ($5500 ×2/100 × 7)
= $5500 + (5500 × 2 × 7/100)
= $5500 + (11000 × 7/100)
= $5500 + (77000/100)
= $5500 + $770 = $6270
Thus, Amount (A) to be paid = $6270 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 7 years
= Simple interest for 1 year × 7
= $110 × 7 = $770
Thus, Simple Interest (SI) = $770
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $770
= $6270
Thus, Amount to be paid = $6270 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 4 years.
(3) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?
(4) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(5) If Mary paid $3416 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.
(8) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.
(9) Susan had to pay $3978.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?