Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.
Correct Answer
$5858
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 2%
Time (t) = 8 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% × 8
= $5050 ×2/100 × 8
= 5050 × 2 × 8/100
= 10100 × 8/100
= 80800/100
= $808
Thus, Simple Interest = $808
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 + $808
= $5858
Thus, Amount to be paid = $5858 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) = 8 years
Thus, Amount (A)
= $5050 + ($5050 × 2% × 8)
= $5050 + ($5050 ×2/100 × 8)
= $5050 + (5050 × 2 × 8/100)
= $5050 + (10100 × 8/100)
= $5050 + (80800/100)
= $5050 + $808 = $5858
Thus, Amount (A) to be paid = $5858 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 8 years
= Simple interest for 1 year × 8
= $101 × 8 = $808
Thus, Simple Interest (SI) = $808
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $808
= $5858
Thus, Amount to be paid = $5858 Answer
Similar Questions
(1) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 4 years.
(2) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.
(3) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7072 to clear the loan, then find the time period of the loan.
(4) Anthony had to pay $4945 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) If Linda paid $4020 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Andrew had to pay $5376 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) How much loan did George borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8030 to clear it?
(8) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.
(9) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.
(10) Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.