Question:
Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
Correct Answer
$10640
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (SI) = 10%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 9
= $5600 ×10/100 × 9
= 5600 × 10 × 9/100
= 56000 × 9/100
= 504000/100
= $5040
Thus, Simple Interest = $5040
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 + $5040
= $10640
Thus, Amount to be paid = $10640 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) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5600 + ($5600 × 10% × 9)
= $5600 + ($5600 ×10/100 × 9)
= $5600 + (5600 × 10 × 9/100)
= $5600 + (56000 × 9/100)
= $5600 + (504000/100)
= $5600 + $5040 = $10640
Thus, Amount (A) to be paid = $10640 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5600, the simple interest in 1 year
= 10/100 × 5600
= 10 × 5600/100
= 56000/100 = $560
Thus, simple interest for 1 year = $560
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $560 × 9 = $5040
Thus, Simple Interest (SI) = $5040
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $5040
= $10640
Thus, Amount to be paid = $10640 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3200 will amount to $3520 at a simple interest of 5% per annum?
(3) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?
(4) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 4 years.
(5) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 5% simple interest?
(6) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(7) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?
(9) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(10) What amount does David have to pay after 5 years if he takes a loan of $3400 at 4% simple interest?