Question:
Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.
Correct Answer
$9976
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 8%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 9
= $5800 ×8/100 × 9
= 5800 × 8 × 9/100
= 46400 × 9/100
= 417600/100
= $4176
Thus, Simple Interest = $4176
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 + $4176
= $9976
Thus, Amount to be paid = $9976 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) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5800 + ($5800 × 8% × 9)
= $5800 + ($5800 ×8/100 × 9)
= $5800 + (5800 × 8 × 9/100)
= $5800 + (46400 × 9/100)
= $5800 + (417600/100)
= $5800 + $4176 = $9976
Thus, Amount (A) to be paid = $9976 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5800, the simple interest in 1 year
= 8/100 × 5800
= 8 × 5800/100
= 46400/100 = $464
Thus, simple interest for 1 year = $464
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $464 × 9 = $4176
Thus, Simple Interest (SI) = $4176
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $4176
= $9976
Thus, Amount to be paid = $9976 Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(2) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
(3) If Barbara paid $3976 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(5) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?
(6) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(7) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 2% simple interest?
(8) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $12000 to clear the loan, then find the time period of the loan.
(9) If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.