Question:
Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 8 years.
Correct Answer
$6728
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 2%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 8
= $5800 ×2/100 × 8
= 5800 × 2 × 8/100
= 11600 × 8/100
= 92800/100
= $928
Thus, Simple Interest = $928
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 + $928
= $6728
Thus, Amount to be paid = $6728 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) = 2%
And, Time (t) = 8 years
Thus, Amount (A)
= $5800 + ($5800 × 2% × 8)
= $5800 + ($5800 ×2/100 × 8)
= $5800 + (5800 × 2 × 8/100)
= $5800 + (11600 × 8/100)
= $5800 + (92800/100)
= $5800 + $928 = $6728
Thus, Amount (A) to be paid = $6728 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5800, the simple interest in 1 year
= 2/100 × 5800
= 2 × 5800/100
= 11600/100 = $116
Thus, simple interest for 1 year = $116
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $116 × 8 = $928
Thus, Simple Interest (SI) = $928
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $928
= $6728
Thus, Amount to be paid = $6728 Answer
Similar Questions
(1) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 6% simple interest?
(2) Patricia had to pay $3622.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Thomas had to pay $4370 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(5) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 5% simple interest?
(6) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
(7) How much loan did Ryan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9875 to clear it?
(8) If Joseph paid $4292 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.
(10) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.