Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 8 years.
Correct Answer
$7070
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 5%
Time (t) = 8 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% × 8
= $5050 ×5/100 × 8
= 5050 × 5 × 8/100
= 25250 × 8/100
= 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) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5050 + ($5050 × 5% × 8)
= $5050 + ($5050 ×5/100 × 8)
= $5050 + (5050 × 5 × 8/100)
= $5050 + (25250 × 8/100)
= $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 = 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 8 years
= Simple interest for 1 year × 8
= $252.5 × 8 = $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) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 8 years.
(2) How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?
(3) 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.
(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 4 years.
(5) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.
(6) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?
(7) Jessica had to pay $3975 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.
(9) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.
(10) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.