Question:
Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.
Correct Answer
$8400
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (SI) = 5%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 10
= $5600 ×5/100 × 10
= 5600 × 5 × 10/100
= 28000 × 10/100
= 280000/100
= $2800
Thus, Simple Interest = $2800
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 + $2800
= $8400
Thus, Amount to be paid = $8400 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) = 5%
And, Time (t) = 10 years
Thus, Amount (A)
= $5600 + ($5600 × 5% × 10)
= $5600 + ($5600 ×5/100 × 10)
= $5600 + (5600 × 5 × 10/100)
= $5600 + (28000 × 10/100)
= $5600 + (280000/100)
= $5600 + $2800 = $8400
Thus, Amount (A) to be paid = $8400 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5600, the simple interest in 1 year
= 5/100 × 5600
= 5 × 5600/100
= 28000/100 = $280
Thus, simple interest for 1 year = $280
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $280 × 10 = $2800
Thus, Simple Interest (SI) = $2800
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $2800
= $8400
Thus, Amount to be paid = $8400 Answer
Similar Questions
(1) How much loan did Amanda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8222.5 to clear it?
(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 3 years.
(3) In how much time a principal of $3000 will amount to $3480 at a simple interest of 4% per annum?
(4) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6120 to clear the loan, then find the time period of the loan.
(5) Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Elizabeth had to pay $3967.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 7 years.
(8) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.
(9) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 4% simple interest?
(10) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.