Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 8 years.
Correct Answer
$8732
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 6%
Time (t) = 8 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) = $5900 × 6% × 8
= $5900 ×6/100 × 8
= 5900 × 6 × 8/100
= 35400 × 8/100
= 283200/100
= $2832
Thus, Simple Interest = $2832
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 = $5900 + $2832
= $8732
Thus, Amount to be paid = $8732 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 = $5900
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5900 + ($5900 × 6% × 8)
= $5900 + ($5900 ×6/100 × 8)
= $5900 + (5900 × 6 × 8/100)
= $5900 + (35400 × 8/100)
= $5900 + (283200/100)
= $5900 + $2832 = $8732
Thus, Amount (A) to be paid = $8732 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 $5900, the simple interest in 1 year
= 6/100 × 5900
= 6 × 5900/100
= 35400/100 = $354
Thus, simple interest for 1 year = $354
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $354 × 8 = $2832
Thus, Simple Interest (SI) = $2832
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $2832
= $8732
Thus, Amount to be paid = $8732 Answer
Similar Questions
(1) How much loan did Nancy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7380 to clear it?
(2) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 8 years.
(3) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.
(4) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?
(5) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 7% simple interest?
(6) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?
(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 8 years.
(8) What amount will be due after 2 years if David borrowed a sum of $3200 at a 8% simple interest?
(9) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
(10) Patricia had to pay $3433.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.