Question:
Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
Correct Answer
$9009
Solution And Explanation
Solution
Given,
Principal (P) = $5850
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) = $5850 × 6% × 9
= $5850 ×6/100 × 9
= 5850 × 6 × 9/100
= 35100 × 9/100
= 315900/100
= $3159
Thus, Simple Interest = $3159
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 = $5850 + $3159
= $9009
Thus, Amount to be paid = $9009 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 = $5850
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5850 + ($5850 × 6% × 9)
= $5850 + ($5850 ×6/100 × 9)
= $5850 + (5850 × 6 × 9/100)
= $5850 + (35100 × 9/100)
= $5850 + (315900/100)
= $5850 + $3159 = $9009
Thus, Amount (A) to be paid = $9009 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 $5850, the simple interest in 1 year
= 6/100 × 5850
= 6 × 5850/100
= 35100/100 = $351
Thus, simple interest for 1 year = $351
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $351 × 9 = $3159
Thus, Simple Interest (SI) = $3159
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $3159
= $9009
Thus, Amount to be paid = $9009 Answer
Similar Questions
(1) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 3 years.
(2) Joshua had to pay $5341 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.
(4) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 3% simple interest?
(5) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.
(6) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.
(8) If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 10% simple interest?
(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 8 years.