Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.
Correct Answer
$7130
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 8
= $5750 ×3/100 × 8
= 5750 × 3 × 8/100
= 17250 × 8/100
= 138000/100
= $1380
Thus, Simple Interest = $1380
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 + $1380
= $7130
Thus, Amount to be paid = $7130 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5750 + ($5750 × 3% × 8)
= $5750 + ($5750 ×3/100 × 8)
= $5750 + (5750 × 3 × 8/100)
= $5750 + (17250 × 8/100)
= $5750 + (138000/100)
= $5750 + $1380 = $7130
Thus, Amount (A) to be paid = $7130 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5750, the simple interest in 1 year
= 3/100 × 5750
= 3 × 5750/100
= 17250/100 = $172.5
Thus, simple interest for 1 year = $172.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $172.5 × 8 = $1380
Thus, Simple Interest (SI) = $1380
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $1380
= $7130
Thus, Amount to be paid = $7130 Answer
Similar Questions
(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.
(2) How much loan did Michael borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5830 to clear it?
(3) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7748 to clear the loan, then find the time period of the loan.
(4) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) 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.
(6) Karen had to pay $4424 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(8) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 10% simple interest?
(9) How much loan did Charles borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6490 to clear it?
(10) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.