Question:
What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 9% simple interest?
Correct Answer
$4851
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 9%
Time (t) = 6 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% × 6
= $3150 ×9/100 × 6
= 3150 × 9 × 6/100
= 28350 × 6/100
= 170100/100
= $1701
Thus, Simple Interest = $1701
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 + $1701
= $4851
Thus, Amount to be paid = $4851 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) = 6 years
Thus, Amount (A)
= $3150 + ($3150 × 9% × 6)
= $3150 + ($3150 ×9/100 × 6)
= $3150 + (3150 × 9 × 6/100)
= $3150 + (28350 × 6/100)
= $3150 + (170100/100)
= $3150 + $1701 = $4851
Thus, Amount (A) to be paid = $4851 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 6 years
= Simple interest for 1 year × 6
= $283.5 × 6 = $1701
Thus, Simple Interest (SI) = $1701
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $1701
= $4851
Thus, Amount to be paid = $4851 Answer
Similar Questions
(1) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 3 years.
(2) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.
(4) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.
(5) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 6% simple interest?
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.
(7) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 6% simple interest?
(8) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 8% simple interest?
(9) If Mary paid $3660 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.