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) Thomas had to pay $4028 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 8 years.
(4) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.
(6) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8692 to clear the loan, then find the time period of the loan.
(7) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 8 years.
(9) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?
(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.