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) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(2) How much loan did Lisa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6655 to clear it?
(3) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.
(5) If Richard borrowed $3600 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(6) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 8% simple interest?
(7) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8364 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 4 years.
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 7 years.
(10) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.