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) If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6300 to clear it?
(3) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.
(4) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.
(5) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 8% simple interest?
(6) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.
(8) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 7 years.
(9) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.
(10) Barbara took a loan of $5100 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.