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 & 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) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 5% simple interest?
(3) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?
(4) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 4 years.
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.