Question:
What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 9% simple interest?
Correct Answer
$4567.5
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 9%
Time (t) = 5 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% × 5
= $3150 ×9/100 × 5
= 3150 × 9 × 5/100
= 28350 × 5/100
= 141750/100
= $1417.5
Thus, Simple Interest = $1417.5
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 + $1417.5
= $4567.5
Thus, Amount to be paid = $4567.5 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) = 5 years
Thus, Amount (A)
= $3150 + ($3150 × 9% × 5)
= $3150 + ($3150 ×9/100 × 5)
= $3150 + (3150 × 9 × 5/100)
= $3150 + (28350 × 5/100)
= $3150 + (141750/100)
= $3150 + $1417.5 = $4567.5
Thus, Amount (A) to be paid = $4567.5 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 5 years
= Simple interest for 1 year × 5
= $283.5 × 5 = $1417.5
Thus, Simple Interest (SI) = $1417.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $1417.5
= $4567.5
Thus, Amount to be paid = $4567.5 Answer
Similar Questions
(1) How much loan did Mark borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8000 to clear it?
(2) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 3 years.
(4) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
(5) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.
(6) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.
(7) How much loan did Mary borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6060 to clear it?
(8) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(9) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(10) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.