Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.
Correct Answer
$8970
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 8%
Time (t) = 7 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% × 7
= $5750 ×8/100 × 7
= 5750 × 8 × 7/100
= 46000 × 7/100
= 322000/100
= $3220
Thus, Simple Interest = $3220
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 + $3220
= $8970
Thus, Amount to be paid = $8970 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) = 7 years
Thus, Amount (A)
= $5750 + ($5750 × 8% × 7)
= $5750 + ($5750 ×8/100 × 7)
= $5750 + (5750 × 8 × 7/100)
= $5750 + (46000 × 7/100)
= $5750 + (322000/100)
= $5750 + $3220 = $8970
Thus, Amount (A) to be paid = $8970 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 7 years
= Simple interest for 1 year × 7
= $460 × 7 = $3220
Thus, Simple Interest (SI) = $3220
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $3220
= $8970
Thus, Amount to be paid = $8970 Answer
Similar Questions
(1) In how much time a principal of $3100 will amount to $3720 at a simple interest of 5% per annum?
(2) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 9% simple interest?
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 8 years.
(4) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 3 years.
(5) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 3 years.
(6) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7975 to clear it?
(7) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.
(8) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 10% simple interest?
(9) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 4 years.
(10) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.