Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 3 years.
Correct Answer
$3717
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 6%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 3
= $3150 ×6/100 × 3
= 3150 × 6 × 3/100
= 18900 × 3/100
= 56700/100
= $567
Thus, Simple Interest = $567
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 + $567
= $3717
Thus, Amount to be paid = $3717 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) = 6%
And, Time (t) = 3 years
Thus, Amount (A)
= $3150 + ($3150 × 6% × 3)
= $3150 + ($3150 ×6/100 × 3)
= $3150 + (3150 × 6 × 3/100)
= $3150 + (18900 × 3/100)
= $3150 + (56700/100)
= $3150 + $567 = $3717
Thus, Amount (A) to be paid = $3717 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $3150, the simple interest in 1 year
= 6/100 × 3150
= 6 × 3150/100
= 18900/100 = $189
Thus, simple interest for 1 year = $189
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $189 × 3 = $567
Thus, Simple Interest (SI) = $567
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $567
= $3717
Thus, Amount to be paid = $3717 Answer
Similar Questions
(1) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 8 years.
(3) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 2% simple interest?
(4) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 3 years.
(6) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.
(8) If Elizabeth borrowed $3450 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) How much loan did Sandra borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7740 to clear it?
(10) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.