Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 7 years.
Correct Answer
$9945
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 10%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 7
= $5850 ×10/100 × 7
= 5850 × 10 × 7/100
= 58500 × 7/100
= 409500/100
= $4095
Thus, Simple Interest = $4095
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 + $4095
= $9945
Thus, Amount to be paid = $9945 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) = 10%
And, Time (t) = 7 years
Thus, Amount (A)
= $5850 + ($5850 × 10% × 7)
= $5850 + ($5850 ×10/100 × 7)
= $5850 + (5850 × 10 × 7/100)
= $5850 + (58500 × 7/100)
= $5850 + (409500/100)
= $5850 + $4095 = $9945
Thus, Amount (A) to be paid = $9945 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5850, the simple interest in 1 year
= 10/100 × 5850
= 10 × 5850/100
= 58500/100 = $585
Thus, simple interest for 1 year = $585
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $585 × 7 = $4095
Thus, Simple Interest (SI) = $4095
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $4095
= $9945
Thus, Amount to be paid = $9945 Answer
Similar Questions
(1) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 8 years.
(2) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 4 years.
(4) If Elizabeth paid $4002 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?
(6) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.
(7) What amount does James have to pay after 6 years if he takes a loan of $3000 at 2% simple interest?
(8) Barbara had to pay $3763 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?
(10) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $10000 to clear the loan, then find the time period of the loan.