Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 8 years.
Correct Answer
$7590
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 4%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 8
= $5750 ×4/100 × 8
= 5750 × 4 × 8/100
= 23000 × 8/100
= 184000/100
= $1840
Thus, Simple Interest = $1840
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 + $1840
= $7590
Thus, Amount to be paid = $7590 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) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5750 + ($5750 × 4% × 8)
= $5750 + ($5750 ×4/100 × 8)
= $5750 + (5750 × 4 × 8/100)
= $5750 + (23000 × 8/100)
= $5750 + (184000/100)
= $5750 + $1840 = $7590
Thus, Amount (A) to be paid = $7590 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5750, the simple interest in 1 year
= 4/100 × 5750
= 4 × 5750/100
= 23000/100 = $230
Thus, simple interest for 1 year = $230
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $230 × 8 = $1840
Thus, Simple Interest (SI) = $1840
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $1840
= $7590
Thus, Amount to be paid = $7590 Answer
Similar Questions
(1) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.
(2) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.
(3) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.
(4) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 4% simple interest?
(6) If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) Sarah had to pay $4196.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9050 to clear the loan, then find the time period of the loan.
(9) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 6% simple interest?
(10) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?