Question:
Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
Correct Answer
$8701
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 6%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 9
= $5650 ×6/100 × 9
= 5650 × 6 × 9/100
= 33900 × 9/100
= 305100/100
= $3051
Thus, Simple Interest = $3051
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 + $3051
= $8701
Thus, Amount to be paid = $8701 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) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5650 + ($5650 × 6% × 9)
= $5650 + ($5650 ×6/100 × 9)
= $5650 + (5650 × 6 × 9/100)
= $5650 + (33900 × 9/100)
= $5650 + (305100/100)
= $5650 + $3051 = $8701
Thus, Amount (A) to be paid = $8701 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5650, the simple interest in 1 year
= 6/100 × 5650
= 6 × 5650/100
= 33900/100 = $339
Thus, simple interest for 1 year = $339
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $339 × 9 = $3051
Thus, Simple Interest (SI) = $3051
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $3051
= $8701
Thus, Amount to be paid = $8701 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.
(2) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7421 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.
(4) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 3 years.
(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 3 years.
(7) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.
(8) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(9) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 3 years.
(10) If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.