Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 8 years.
Correct Answer
$9430
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 8%
Time (t) = 8 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) = $5750 × 8% × 8
= $5750 ×8/100 × 8
= 5750 × 8 × 8/100
= 46000 × 8/100
= 368000/100
= $3680
Thus, Simple Interest = $3680
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 + $3680
= $9430
Thus, Amount to be paid = $9430 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) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5750 + ($5750 × 8% × 8)
= $5750 + ($5750 ×8/100 × 8)
= $5750 + (5750 × 8 × 8/100)
= $5750 + (46000 × 8/100)
= $5750 + (368000/100)
= $5750 + $3680 = $9430
Thus, Amount (A) to be paid = $9430 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 $5750, the simple interest in 1 year
= 8/100 × 5750
= 8 × 5750/100
= 46000/100 = $460
Thus, simple interest for 1 year = $460
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $460 × 8 = $3680
Thus, Simple Interest (SI) = $3680
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $3680
= $9430
Thus, Amount to be paid = $9430 Answer
Similar Questions
(1) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 3 years.
(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 7 years.
(3) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.
(4) In how much time a principal of $3150 will amount to $3276 at a simple interest of 2% per annum?
(5) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?
(6) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 8% simple interest?
(7) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 3 years.
(8) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(9) If Joseph paid $4144 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?