Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.
Correct Answer
$3433.5
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 3%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 3
= $3150 ×3/100 × 3
= 3150 × 3 × 3/100
= 9450 × 3/100
= 28350/100
= $283.5
Thus, Simple Interest = $283.5
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 + $283.5
= $3433.5
Thus, Amount to be paid = $3433.5 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) = 3%
And, Time (t) = 3 years
Thus, Amount (A)
= $3150 + ($3150 × 3% × 3)
= $3150 + ($3150 ×3/100 × 3)
= $3150 + (3150 × 3 × 3/100)
= $3150 + (9450 × 3/100)
= $3150 + (28350/100)
= $3150 + $283.5 = $3433.5
Thus, Amount (A) to be paid = $3433.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3150, the simple interest in 1 year
= 3/100 × 3150
= 3 × 3150/100
= 9450/100 = $94.5
Thus, simple interest for 1 year = $94.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $94.5 × 3 = $283.5
Thus, Simple Interest (SI) = $283.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $283.5
= $3433.5
Thus, Amount to be paid = $3433.5 Answer
Similar Questions
(1) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?
(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.
(3) In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?
(4) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 7 years.
(6) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
(8) If Barbara borrowed $3550 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 6% simple interest?
(10) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.