Question:
Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.
Correct Answer
$10640
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (SI) = 9%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 10
= $5600 ×9/100 × 10
= 5600 × 9 × 10/100
= 50400 × 10/100
= 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) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5600 + ($5600 × 9% × 10)
= $5600 + ($5600 ×9/100 × 10)
= $5600 + (5600 × 9 × 10/100)
= $5600 + (50400 × 10/100)
= $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 = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5600, the simple interest in 1 year
= 9/100 × 5600
= 9 × 5600/100
= 50400/100 = $504
Thus, simple interest for 1 year = $504
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $504 × 10 = $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) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(2) William had to pay $3710 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(4) Steven had to pay $5014 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.
(6) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.
(7) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 2% simple interest?
(8) What amount does James have to pay after 6 years if he takes a loan of $3000 at 3% simple interest?
(9) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 4% simple interest?