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) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(2) If Susan paid $4380 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Lisa had to pay $4293 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
(5) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 3 years.
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.
(7) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 4 years.
(8) How much loan did Patricia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6180 to clear it?
(9) If James paid $3480 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.