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) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 7 years.
(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 2% simple interest?
(4) How much loan did Donald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8125 to clear it?
(5) Joshua had to pay $5488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?
(7) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.
(8) In how much time a principal of $3200 will amount to $3584 at a simple interest of 4% per annum?
(9) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.
(10) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.