Question:
Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.
Correct Answer
$7070
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 4%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 10
= $5050 ×4/100 × 10
= 5050 × 4 × 10/100
= 20200 × 10/100
= 202000/100
= $2020
Thus, Simple Interest = $2020
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 + $2020
= $7070
Thus, Amount to be paid = $7070 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) = 4%
And, Time (t) = 10 years
Thus, Amount (A)
= $5050 + ($5050 × 4% × 10)
= $5050 + ($5050 ×4/100 × 10)
= $5050 + (5050 × 4 × 10/100)
= $5050 + (20200 × 10/100)
= $5050 + (202000/100)
= $5050 + $2020 = $7070
Thus, Amount (A) to be paid = $7070 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5050, the simple interest in 1 year
= 4/100 × 5050
= 4 × 5050/100
= 20200/100 = $202
Thus, simple interest for 1 year = $202
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $202 × 10 = $2020
Thus, Simple Interest (SI) = $2020
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $2020
= $7070
Thus, Amount to be paid = $7070 Answer
Similar Questions
(1) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 7% simple interest?
(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 7 years.
(3) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 3 years.
(4) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10824 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 7 years.
(6) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 4 years.
(7) How much loan did Deborah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8195 to clear it?
(8) Lisa had to pay $4657.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(10) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.