Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.
Correct Answer
$3906
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 8%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 3
= $3150 ×8/100 × 3
= 3150 × 8 × 3/100
= 25200 × 3/100
= 75600/100
= $756
Thus, Simple Interest = $756
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 + $756
= $3906
Thus, Amount to be paid = $3906 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) = 8%
And, Time (t) = 3 years
Thus, Amount (A)
= $3150 + ($3150 × 8% × 3)
= $3150 + ($3150 ×8/100 × 3)
= $3150 + (3150 × 8 × 3/100)
= $3150 + (25200 × 3/100)
= $3150 + (75600/100)
= $3150 + $756 = $3906
Thus, Amount (A) to be paid = $3906 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $3150, the simple interest in 1 year
= 8/100 × 3150
= 8 × 3150/100
= 25200/100 = $252
Thus, simple interest for 1 year = $252
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $252 × 3 = $756
Thus, Simple Interest (SI) = $756
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $756
= $3906
Thus, Amount to be paid = $3906 Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7152 to clear the loan, then find the time period of the loan.
(2) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 4% simple interest?
(4) How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?
(5) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.
(6) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 8% simple interest?
(7) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.
(8) If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
(10) How much loan did Daniel borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7320 to clear it?