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) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.
(2) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 3 years.
(4) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 3 years.
(5) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?
(6) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 4% simple interest?
(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 3 years.
(8) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 4 years.
(10) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.