Question:
Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 8 years.
Correct Answer
$9976
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 9%
Time (t) = 8 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% × 8
= $5800 ×9/100 × 8
= 5800 × 9 × 8/100
= 52200 × 8/100
= 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) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5800 + ($5800 × 9% × 8)
= $5800 + ($5800 ×9/100 × 8)
= $5800 + (5800 × 9 × 8/100)
= $5800 + (52200 × 8/100)
= $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 = 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 8 years
= Simple interest for 1 year × 8
= $522 × 8 = $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) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 10% simple interest?
(2) What amount does James have to pay after 6 years if he takes a loan of $3000 at 5% simple interest?
(3) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 7% simple interest?
(4) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(5) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 8 years.
(7) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(8) If Nancy paid $4980 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9955 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 7 years.