Question:
Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 8 years.
Correct Answer
$9512
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 8%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $5800 × 8% × 8
= $5800 ×8/100 × 8
= 5800 × 8 × 8/100
= 46400 × 8/100
= 371200/100
= $3712
Thus, Simple Interest = $3712
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 = $5800 + $3712
= $9512
Thus, Amount to be paid = $9512 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 = $5800
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5800 + ($5800 × 8% × 8)
= $5800 + ($5800 ×8/100 × 8)
= $5800 + (5800 × 8 × 8/100)
= $5800 + (46400 × 8/100)
= $5800 + (371200/100)
= $5800 + $3712 = $9512
Thus, Amount (A) to be paid = $9512 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5800, the simple interest in 1 year
= 8/100 × 5800
= 8 × 5800/100
= 46400/100 = $464
Thus, simple interest for 1 year = $464
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $464 × 8 = $3712
Thus, Simple Interest (SI) = $3712
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $3712
= $9512
Thus, Amount to be paid = $9512 Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.
(3) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?
(4) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11584 to clear the loan, then find the time period of the loan.
(5) Thomas had to pay $4142 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 3% simple interest?
(7) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?
(8) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.
(9) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 7% simple interest?
(10) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 6% simple interest?