Question:
Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 8 years.
Correct Answer
$8736
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (SI) = 7%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 8
= $5600 ×7/100 × 8
= 5600 × 7 × 8/100
= 39200 × 8/100
= 313600/100
= $3136
Thus, Simple Interest = $3136
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 + $3136
= $8736
Thus, Amount to be paid = $8736 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) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5600 + ($5600 × 7% × 8)
= $5600 + ($5600 ×7/100 × 8)
= $5600 + (5600 × 7 × 8/100)
= $5600 + (39200 × 8/100)
= $5600 + (313600/100)
= $5600 + $3136 = $8736
Thus, Amount (A) to be paid = $8736 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5600, the simple interest in 1 year
= 7/100 × 5600
= 7 × 5600/100
= 39200/100 = $392
Thus, simple interest for 1 year = $392
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $392 × 8 = $3136
Thus, Simple Interest (SI) = $3136
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $3136
= $8736
Thus, Amount to be paid = $8736 Answer
Similar Questions
(1) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 6% simple interest?
(2) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.
(3) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.
(4) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.
(5) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.
(6) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.
(7) Joshua had to pay $5488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 4 years.
(9) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?
(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 7 years.