Question:
Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.
Correct Answer
$7820
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 4%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 9
= $5750 ×4/100 × 9
= 5750 × 4 × 9/100
= 23000 × 9/100
= 207000/100
= $2070
Thus, Simple Interest = $2070
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 + $2070
= $7820
Thus, Amount to be paid = $7820 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) = 4%
And, Time (t) = 9 years
Thus, Amount (A)
= $5750 + ($5750 × 4% × 9)
= $5750 + ($5750 ×4/100 × 9)
= $5750 + (5750 × 4 × 9/100)
= $5750 + (23000 × 9/100)
= $5750 + (207000/100)
= $5750 + $2070 = $7820
Thus, Amount (A) to be paid = $7820 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5750, the simple interest in 1 year
= 4/100 × 5750
= 4 × 5750/100
= 23000/100 = $230
Thus, simple interest for 1 year = $230
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $230 × 9 = $2070
Thus, Simple Interest (SI) = $2070
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $2070
= $7820
Thus, Amount to be paid = $7820 Answer
Similar Questions
(1) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 3 years.
(2) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 4 years.
(3) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(4) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?
(5) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 3% simple interest?
(6) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.
(7) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 5% simple interest?
(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 8 years.
(9) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 4 years.