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) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 9% simple interest?
(2) If Michael borrowed $3300 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(3) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?
(4) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.
(5) If Christopher paid $4640 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11152 to clear the loan, then find the time period of the loan.
(7) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.
(8) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 8 years.
(10) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.