Question:
Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
Correct Answer
$6060
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 2%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 10
= $5050 ×2/100 × 10
= 5050 × 2 × 10/100
= 10100 × 10/100
= 101000/100
= $1010
Thus, Simple Interest = $1010
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 + $1010
= $6060
Thus, Amount to be paid = $6060 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) = 2%
And, Time (t) = 10 years
Thus, Amount (A)
= $5050 + ($5050 × 2% × 10)
= $5050 + ($5050 ×2/100 × 10)
= $5050 + (5050 × 2 × 10/100)
= $5050 + (10100 × 10/100)
= $5050 + (101000/100)
= $5050 + $1010 = $6060
Thus, Amount (A) to be paid = $6060 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5050, the simple interest in 1 year
= 2/100 × 5050
= 2 × 5050/100
= 10100/100 = $101
Thus, simple interest for 1 year = $101
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $101 × 10 = $1010
Thus, Simple Interest (SI) = $1010
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $1010
= $6060
Thus, Amount to be paid = $6060 Answer
Similar Questions
(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 8 years.
(2) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
(4) How much loan did Matthew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6820 to clear it?
(5) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.
(6) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9184 to clear the loan, then find the time period of the loan.
(7) What amount does William have to pay after 6 years if he takes a loan of $3500 at 5% simple interest?
(8) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
(9) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 6% simple interest?
(10) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.