Question:
Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 8 years.
Correct Answer
$7006
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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) = $5650 × 3% × 8
= $5650 ×3/100 × 8
= 5650 × 3 × 8/100
= 16950 × 8/100
= 135600/100
= $1356
Thus, Simple Interest = $1356
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 = $5650 + $1356
= $7006
Thus, Amount to be paid = $7006 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 = $5650
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5650 + ($5650 × 3% × 8)
= $5650 + ($5650 ×3/100 × 8)
= $5650 + (5650 × 3 × 8/100)
= $5650 + (16950 × 8/100)
= $5650 + (135600/100)
= $5650 + $1356 = $7006
Thus, Amount (A) to be paid = $7006 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5650, the simple interest in 1 year
= 3/100 × 5650
= 3 × 5650/100
= 16950/100 = $169.5
Thus, simple interest for 1 year = $169.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $169.5 × 8 = $1356
Thus, Simple Interest (SI) = $1356
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $1356
= $7006
Thus, Amount to be paid = $7006 Answer
Similar Questions
(1) Michael had to pay $3696 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 4 years.
(3) How much loan did Karen borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7140 to clear it?
(4) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?
(5) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?
(6) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.
(7) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.
(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 7 years.
(10) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.