Question:
Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 7 years.
Correct Answer
$9048
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 8%
Time (t) = 7 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% × 7
= $5800 ×8/100 × 7
= 5800 × 8 × 7/100
= 46400 × 7/100
= 324800/100
= $3248
Thus, Simple Interest = $3248
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 + $3248
= $9048
Thus, Amount to be paid = $9048 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) = 7 years
Thus, Amount (A)
= $5800 + ($5800 × 8% × 7)
= $5800 + ($5800 ×8/100 × 7)
= $5800 + (5800 × 8 × 7/100)
= $5800 + (46400 × 7/100)
= $5800 + (324800/100)
= $5800 + $3248 = $9048
Thus, Amount (A) to be paid = $9048 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 7 years
= Simple interest for 1 year × 7
= $464 × 7 = $3248
Thus, Simple Interest (SI) = $3248
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $3248
= $9048
Thus, Amount to be paid = $9048 Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 8 years.
(3) If Betty paid $5100 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 4 years.
(5) Jessica had to pay $4200 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3150 will amount to $3937.5 at a simple interest of 5% per annum?
(8) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 10% simple interest?
(9) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(10) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?