Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 7 years.
Correct Answer
$6957.5
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 3%
Time (t) = 7 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% × 7
= $5750 ×3/100 × 7
= 5750 × 3 × 7/100
= 17250 × 7/100
= 120750/100
= $1207.5
Thus, Simple Interest = $1207.5
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 + $1207.5
= $6957.5
Thus, Amount to be paid = $6957.5 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) = 7 years
Thus, Amount (A)
= $5750 + ($5750 × 3% × 7)
= $5750 + ($5750 ×3/100 × 7)
= $5750 + (5750 × 3 × 7/100)
= $5750 + (17250 × 7/100)
= $5750 + (120750/100)
= $5750 + $1207.5 = $6957.5
Thus, Amount (A) to be paid = $6957.5 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 7 years
= Simple interest for 1 year × 7
= $172.5 × 7 = $1207.5
Thus, Simple Interest (SI) = $1207.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $1207.5
= $6957.5
Thus, Amount to be paid = $6957.5 Answer
Similar Questions
(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.
(2) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.
(3) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?
(4) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 2% simple interest?
(5) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.
(7) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(8) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 3 years.
(9) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?
(10) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?