Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.
Correct Answer
$9775
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 10%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 7
= $5750 ×10/100 × 7
= 5750 × 10 × 7/100
= 57500 × 7/100
= 402500/100
= $4025
Thus, Simple Interest = $4025
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 + $4025
= $9775
Thus, Amount to be paid = $9775 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) = 10%
And, Time (t) = 7 years
Thus, Amount (A)
= $5750 + ($5750 × 10% × 7)
= $5750 + ($5750 ×10/100 × 7)
= $5750 + (5750 × 10 × 7/100)
= $5750 + (57500 × 7/100)
= $5750 + (402500/100)
= $5750 + $4025 = $9775
Thus, Amount (A) to be paid = $9775 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5750, the simple interest in 1 year
= 10/100 × 5750
= 10 × 5750/100
= 57500/100 = $575
Thus, simple interest for 1 year = $575
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $575 × 7 = $4025
Thus, Simple Interest (SI) = $4025
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $4025
= $9775
Thus, Amount to be paid = $9775 Answer
Similar Questions
(1) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.
(2) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 5% simple interest?
(3) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8432 to clear the loan, then find the time period of the loan.
(4) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6556 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 4 years.
(6) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 8% simple interest?
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 7 years.
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 8 years.
(9) How much loan did Edward borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8740 to clear it?
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 3 years.