Question:
What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 6% simple interest?
Correct Answer
$4284
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 6%
Time (t) = 6 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% × 6
= $3150 ×6/100 × 6
= 3150 × 6 × 6/100
= 18900 × 6/100
= 113400/100
= $1134
Thus, Simple Interest = $1134
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 + $1134
= $4284
Thus, Amount to be paid = $4284 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) = 6 years
Thus, Amount (A)
= $3150 + ($3150 × 6% × 6)
= $3150 + ($3150 ×6/100 × 6)
= $3150 + (3150 × 6 × 6/100)
= $3150 + (18900 × 6/100)
= $3150 + (113400/100)
= $3150 + $1134 = $4284
Thus, Amount (A) to be paid = $4284 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 6 years
= Simple interest for 1 year × 6
= $189 × 6 = $1134
Thus, Simple Interest (SI) = $1134
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $1134
= $4284
Thus, Amount to be paid = $4284 Answer
Similar Questions
(1) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 3 years.
(2) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.
(3) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(4) How much loan did Ryan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8690 to clear it?
(5) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 8 years.
(6) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 3 years.
(8) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(9) If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 8 years.