Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.
Correct Answer
$7254
Solution And Explanation
Solution
Given,
Principal (P) = $5850
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) = $5850 × 3% × 8
= $5850 ×3/100 × 8
= 5850 × 3 × 8/100
= 17550 × 8/100
= 140400/100
= $1404
Thus, Simple Interest = $1404
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 + $1404
= $7254
Thus, Amount to be paid = $7254 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5850 + ($5850 × 3% × 8)
= $5850 + ($5850 ×3/100 × 8)
= $5850 + (5850 × 3 × 8/100)
= $5850 + (17550 × 8/100)
= $5850 + (140400/100)
= $5850 + $1404 = $7254
Thus, Amount (A) to be paid = $7254 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 $5850, the simple interest in 1 year
= 3/100 × 5850
= 3 × 5850/100
= 17550/100 = $175.5
Thus, simple interest for 1 year = $175.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $175.5 × 8 = $1404
Thus, Simple Interest (SI) = $1404
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $1404
= $7254
Thus, Amount to be paid = $7254 Answer
Similar Questions
(1) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 2% simple interest?
(2) If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
(4) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?
(5) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
(6) In how much time a principal of $3100 will amount to $3348 at a simple interest of 2% per annum?
(7) Donald had to pay $4905 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 6% simple interest?
(9) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 7 years.
(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 4 years.