Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 3 years.
Correct Answer
$4000.5
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 9%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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) = $3150 × 9% × 3
= $3150 ×9/100 × 3
= 3150 × 9 × 3/100
= 28350 × 3/100
= 85050/100
= $850.5
Thus, Simple Interest = $850.5
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 = $3150 + $850.5
= $4000.5
Thus, Amount to be paid = $4000.5 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 = $3150
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 3 years
Thus, Amount (A)
= $3150 + ($3150 × 9% × 3)
= $3150 + ($3150 ×9/100 × 3)
= $3150 + (3150 × 9 × 3/100)
= $3150 + (28350 × 3/100)
= $3150 + (85050/100)
= $3150 + $850.5 = $4000.5
Thus, Amount (A) to be paid = $4000.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $3150, the simple interest in 1 year
= 9/100 × 3150
= 9 × 3150/100
= 28350/100 = $283.5
Thus, simple interest for 1 year = $283.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $283.5 × 3 = $850.5
Thus, Simple Interest (SI) = $850.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $850.5
= $4000.5
Thus, Amount to be paid = $4000.5 Answer
Similar Questions
(1) Matthew had to pay $4830 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 2% simple interest?
(3) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 7% simple interest?
(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 8 years.
(5) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 7 years.
(7) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.
(8) What amount does William have to pay after 6 years if he takes a loan of $3500 at 7% simple interest?
(9) Paul had to pay $5264 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 4 years.