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) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.
(2) If Jennifer paid $3900 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.
(4) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.
(6) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?
(7) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.
(9) If Michael borrowed $3300 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 7 years.