Question:
Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 8 years.
Correct Answer
$10080
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (SI) = 10%
Time (t) = 8 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% × 8
= $5600 ×10/100 × 8
= 5600 × 10 × 8/100
= 56000 × 8/100
= 448000/100
= $4480
Thus, Simple Interest = $4480
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 + $4480
= $10080
Thus, Amount to be paid = $10080 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) = 8 years
Thus, Amount (A)
= $5600 + ($5600 × 10% × 8)
= $5600 + ($5600 ×10/100 × 8)
= $5600 + (5600 × 10 × 8/100)
= $5600 + (56000 × 8/100)
= $5600 + (448000/100)
= $5600 + $4480 = $10080
Thus, Amount (A) to be paid = $10080 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 8 years
= Simple interest for 1 year × 8
= $560 × 8 = $4480
Thus, Simple Interest (SI) = $4480
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $4480
= $10080
Thus, Amount to be paid = $10080 Answer
Similar Questions
(1) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 4 years.
(2) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(3) If Jennifer borrowed $3250 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(4) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.
(6) What amount will be due after 2 years if William borrowed a sum of $3250 at a 6% simple interest?
(7) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.
(8) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?
(9) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7301 to clear the loan, then find the time period of the loan.
(10) If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.