Question:
Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.
Correct Answer
$10498
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 9%
Time (t) = 9 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) = $5800 × 9% × 9
= $5800 ×9/100 × 9
= 5800 × 9 × 9/100
= 52200 × 9/100
= 469800/100
= $4698
Thus, Simple Interest = $4698
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 = $5800 + $4698
= $10498
Thus, Amount to be paid = $10498 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 = $5800
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 9 years
Thus, Amount (A)
= $5800 + ($5800 × 9% × 9)
= $5800 + ($5800 ×9/100 × 9)
= $5800 + (5800 × 9 × 9/100)
= $5800 + (52200 × 9/100)
= $5800 + (469800/100)
= $5800 + $4698 = $10498
Thus, Amount (A) to be paid = $10498 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 $5800, the simple interest in 1 year
= 9/100 × 5800
= 9 × 5800/100
= 52200/100 = $522
Thus, simple interest for 1 year = $522
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $522 × 9 = $4698
Thus, Simple Interest (SI) = $4698
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $4698
= $10498
Thus, Amount to be paid = $10498 Answer
Similar Questions
(1) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 2% simple interest?
(2) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.
(3) Joseph had to pay $4033 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.
(5) How much loan did Steven borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7260 to clear it?
(6) Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 3% simple interest?
(8) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?
(9) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 9% simple interest?
(10) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.