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) Susan had to pay $4197.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 8 years.
(3) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 8% simple interest?
(4) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 6% simple interest?
(5) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.
(6) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(7) If Michelle paid $5346 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 9% simple interest?
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 7 years.