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) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
(2) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 8% simple interest.
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 7 years.
(4) How much loan did Sarah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6435 to clear it?
(5) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.
(6) How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?
(7) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 6% simple interest?
(8) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?
(9) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(10) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.