Question:
Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 8 years.
Correct Answer
$9184
Solution And Explanation
Solution
Given,
Principal (P) = $5600
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) = $5600 × 8% × 8
= $5600 ×8/100 × 8
= 5600 × 8 × 8/100
= 44800 × 8/100
= 358400/100
= $3584
Thus, Simple Interest = $3584
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 = $5600 + $3584
= $9184
Thus, Amount to be paid = $9184 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 = $5600
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5600 + ($5600 × 8% × 8)
= $5600 + ($5600 ×8/100 × 8)
= $5600 + (5600 × 8 × 8/100)
= $5600 + (44800 × 8/100)
= $5600 + (358400/100)
= $5600 + $3584 = $9184
Thus, Amount (A) to be paid = $9184 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 $5600, the simple interest in 1 year
= 8/100 × 5600
= 8 × 5600/100
= 44800/100 = $448
Thus, simple interest for 1 year = $448
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $448 × 8 = $3584
Thus, Simple Interest (SI) = $3584
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $3584
= $9184
Thus, Amount to be paid = $9184 Answer
Similar Questions
(1) What amount will be due after 2 years if James borrowed a sum of $3000 at a 4% simple interest?
(2) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
(3) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(4) In how much time a principal of $3200 will amount to $4000 at a simple interest of 5% per annum?
(5) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.
(6) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 6% simple interest?
(7) John had to pay $3488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 8 years.
(9) How much loan did Laura borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9027.5 to clear it?
(10) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 10% simple interest.