Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 7 years.
Correct Answer
$6817.5
Solution And Explanation
Solution
Given,
Principal (P) = $5050
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) = $5050 × 5% × 7
= $5050 ×5/100 × 7
= 5050 × 5 × 7/100
= 25250 × 7/100
= 176750/100
= $1767.5
Thus, Simple Interest = $1767.5
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 = $5050 + $1767.5
= $6817.5
Thus, Amount to be paid = $6817.5 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 = $5050
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $5050 + ($5050 × 5% × 7)
= $5050 + ($5050 ×5/100 × 7)
= $5050 + (5050 × 5 × 7/100)
= $5050 + (25250 × 7/100)
= $5050 + (176750/100)
= $5050 + $1767.5 = $6817.5
Thus, Amount (A) to be paid = $6817.5 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 $5050, the simple interest in 1 year
= 5/100 × 5050
= 5 × 5050/100
= 25250/100 = $252.5
Thus, simple interest for 1 year = $252.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $252.5 × 7 = $1767.5
Thus, Simple Interest (SI) = $1767.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $1767.5
= $6817.5
Thus, Amount to be paid = $6817.5 Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 7 years.
(3) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(4) How much loan did Jason borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8855 to clear it?
(5) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?
(6) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) In how much time a principal of $3200 will amount to $3584 at a simple interest of 4% per annum?
(8) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 4 years.
(9) How much loan did Matthew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7440 to clear it?
(10) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.