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 Susan have to pay after 5 years if he takes a loan of $3650 at 10% simple interest?
(2) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 4 years.
(4) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 6% simple interest?
(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 4 years.
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 8 years.
(7) What amount will be due after 2 years if David borrowed a sum of $3200 at a 6% simple interest?
(8) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.
(9) If John paid $3584 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 4 years.