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) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(2) How much loan did Christopher borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6600 to clear it?
(3) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 5% simple interest.
(4) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?
(5) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6888 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 8 years.
(7) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 8 years.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 4 years.
(10) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?