Question:
Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.
Correct Answer
$7575
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 5%
Time (t) = 10 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% × 10
= $5050 ×5/100 × 10
= 5050 × 5 × 10/100
= 25250 × 10/100
= 252500/100
= $2525
Thus, Simple Interest = $2525
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 + $2525
= $7575
Thus, Amount to be paid = $7575 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) = 10 years
Thus, Amount (A)
= $5050 + ($5050 × 5% × 10)
= $5050 + ($5050 ×5/100 × 10)
= $5050 + (5050 × 5 × 10/100)
= $5050 + (25250 × 10/100)
= $5050 + (252500/100)
= $5050 + $2525 = $7575
Thus, Amount (A) to be paid = $7575 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 10 years
= Simple interest for 1 year × 10
= $252.5 × 10 = $2525
Thus, Simple Interest (SI) = $2525
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $2525
= $7575
Thus, Amount to be paid = $7575 Answer
Similar Questions
(1) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 5% per annum?
(2) Sarah had to pay $4312 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?
(4) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 7 years.
(6) 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?
(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?
(8) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.
(9) Sandra had to pay $5117.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.