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) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.
(2) Mary had to pay $3507.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(4) If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 8 years.
(6) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?
(8) In how much time a principal of $3000 will amount to $3240 at a simple interest of 4% per annum?
(9) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?
(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 8 years.