Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 8 years.
Correct Answer
$8510
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 6%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $5750 × 6% × 8
= $5750 ×6/100 × 8
= 5750 × 6 × 8/100
= 34500 × 8/100
= 276000/100
= $2760
Thus, Simple Interest = $2760
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 = $5750 + $2760
= $8510
Thus, Amount to be paid = $8510 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 = $5750
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5750 + ($5750 × 6% × 8)
= $5750 + ($5750 ×6/100 × 8)
= $5750 + (5750 × 6 × 8/100)
= $5750 + (34500 × 8/100)
= $5750 + (276000/100)
= $5750 + $2760 = $8510
Thus, Amount (A) to be paid = $8510 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5750, the simple interest in 1 year
= 6/100 × 5750
= 6 × 5750/100
= 34500/100 = $345
Thus, simple interest for 1 year = $345
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $345 × 8 = $2760
Thus, Simple Interest (SI) = $2760
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $2760
= $8510
Thus, Amount to be paid = $8510 Answer
Similar Questions
(1) If Nancy paid $4814 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 8% simple interest?
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 8 years.
(4) If David borrowed $3400 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(5) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 7% simple interest?
(6) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 6% simple interest?
(7) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10136 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 7 years.
(9) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11800 to clear the loan, then find the time period of the loan.
(10) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.