Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 8 years.
Correct Answer
$8686
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 9%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 8
= $5050 ×9/100 × 8
= 5050 × 9 × 8/100
= 45450 × 8/100
= 363600/100
= $3636
Thus, Simple Interest = $3636
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 + $3636
= $8686
Thus, Amount to be paid = $8686 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) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5050 + ($5050 × 9% × 8)
= $5050 + ($5050 ×9/100 × 8)
= $5050 + (5050 × 9 × 8/100)
= $5050 + (45450 × 8/100)
= $5050 + (363600/100)
= $5050 + $3636 = $8686
Thus, Amount (A) to be paid = $8686 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5050, the simple interest in 1 year
= 9/100 × 5050
= 9 × 5050/100
= 45450/100 = $454.5
Thus, simple interest for 1 year = $454.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $454.5 × 8 = $3636
Thus, Simple Interest (SI) = $3636
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $3636
= $8686
Thus, Amount to be paid = $8686 Answer
Similar Questions
(1) How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?
(2) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?
(3) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 8 years.
(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(6) Lisa had to pay $4536 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Ashley had to pay $4959.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Paul had to pay $5264 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 3 years.